Study Guide and Intervention
|
|
- Erick O’Connor’
- 6 years ago
- Views:
Transcription
1 IO 1-1 tudy Guide and Intervention oints, Lines, and lanes ame oints, Lines, and lanes In geometry, a point is a location, a line contains points, and a plane is a flat surface that contains points and lines. If points are on the same line, they are collinear. If points on are the same plane, they are coplanar. xample a. a line containing point Use the figure to name each of the following. he line can be named as. lso, any two of the three points on the line can be used to name it.,, or b. a plane containing point he plane can be named as plane or can be named using three noncollinear points in the plane, such as plane, plane, and so on. Lesson 1-1 xercises efer to the figure. 1. ame a line that contains point. 2. What is another name for line m? m 3. ame a point not on. 4. ame the intersection of and. 5. ame a point not on line or line m. raw and label a plane for each relationship. 6. is in plane. 7. intersects at. X Y 8. oint X is collinear with points and. 9. oint Y is not collinear with points and. 10. Line contains points X and Y. Glencoe/cGraw-Hill 1 Glencoe Geometry
2 IO 1-1 tudy Guide and Intervention (continued) oints, Lines, and lanes oints, Lines, and lanes in pace pace is a boundless, three-dimensional set of all points. It contains lines and planes. xample a. How many planes appear in the figure? O here are three planes: plane, plane O, and plane. b. re points,, and coplanar? Yes. hey are contained in plane O. xercises efer to the figure. 1. ame a line that is not contained in plane. 2. ame a plane that contains point. 3. ame three collinear points. efer to the figure. 4. How many planes are shown in the figure? 5. re points,, G, and H coplanar? xplain. G J H I 6. ame a point coplanar with,, and. raw and label a figure for each relationship. 7. lanes and intersect in HJ. t s 8. Line r is in plane, line s is in plane, and lines r and s intersect at point J. H J r 9. Line t contains point H and line t does not lie in plane or plane. Glencoe/cGraw-Hill 2 Glencoe Geometry
3 1-1 IO kills ractice efer to the figure. oints, Lines, and lanes 1. ame a line that contains point. 2. ame a point contained in line n. p n G 3. What is another name for line p? 4. ame the plane containing lines n and p. Lesson 1-1 raw and label a figure for each relationship. 5. oint K lies on. 6. lane J contains line s. K J s 7. Y lies in plane and contains point, but does not contain point H. in plane U. Y H 8. Lines q and f intersect at point Z U q Z f efer to the figure. 9. How many planes are shown in the figure? 10. How many of the planes contain points and? W 11. ame four points that are coplanar. 12. re points,, and coplanar? xplain. Glencoe/cGraw-Hill 3 Glencoe Geometry
4 1-1 IO ractice efer to the figure. oints, Lines, and lanes 1. ame a line that contains points and. 2. ame a line that intersects the plane containing points,, and. j g h 3. ame the plane that contains and. raw and label a figure for each relationship. 4. K and G intersect at point in plane. K G 5. line contains L( 4, 4) and (2, 3). Line q is in the same coordinate plane but does not intersect L. Line q contains point. y q O x L efer to the figure. 6. How many planes are shown in the figure? 7. ame three collinear points. W X 8. re points,,, and W coplanar? xplain. VIULIZIO ame the geometric term(s) modeled by each object tip of pin 11. O strings 12. a car antenna 13. a library card Glencoe/cGraw-Hill 4 Glencoe Geometry
5 1-2 IO tudy Guide and Intervention Linear easure and recision easure Line egments part of a line between two endpoints is called a line segment. he lengths of and are written as and. When you measure a segment, the precision of the measurement is half of the smallest unit on the ruler. xample 1 xample 2 ind the length of. ind the length of. cm in. 1 2 he long marks are centimeters, and the shorter marks are millimeters. he length of is 3.4 centimeters. he measurement is accurate to within 0.5 millimeter, so is between 3.35 centimeters and 3.45 centimeters long. xercises he long marks are inches and the short marks are quarter inches. he length of is about inches. he measurement is accurate to within one half of a quarter inch, or 1 8 inch, so is between 1 5 inches and ind the length of each line segment or object. inches long. Lesson cm in in. 1 2 cm ind the precision for each measurement in mm cm 8. 2 ft mm yd 2 Glencoe/cGraw-Hill 7 Glencoe Geometry
6 1-2 IO tudy Guide and Intervention (continued) Linear easure and recision alculate easures On, to say that point is between points and means,, and are collinear and. On, 3 cm. We can say that the segments are congruent, or. lashes on the figure indicate which segments are congruent. xample 1 xample 2 ind. ind x and. 1.2 cm 1.9 cm alculate by adding and herefore, is 3.1 centimeters long. 2x 5 x 2x is between and. x 2x 2x 5 3x 2x 5 x 5 2x 5 2(5) 5 15 xercises ind the measurement of each segment. ssume that the art is not drawn to scale cm 2.5 cm in. 6 in. 3. X Z 3 4. W X 31 2 in. 4 in. X Y Z W 6 cm X Y ind x and if is between and. 5. 5x, 3x, and x, 5x 4, and x, 12, and x,, and 24. Use the figures to determine whether each pair of segments is congruent. 9. and 11 cm 10. X Y and Y Z X 5 cm 5 cm 3x 5 5x 1 11 cm Y 9x 2 Z Glencoe/cGraw-Hill 8 Glencoe Geometry
7 1-2 IO kills ractice Linear easure and recision ind the length of each line segment or object cm in. 1 2 ind the precision for each measurement feet centimeters inches 2 ind the measurement of each segment G H 1in in. 4.9 cm 5.2 cm 9.7 mm G H 15 mm Lesson 1-2 ind the value of the variable and YZ if Y is between X and Z. 9. XY 5p, YZ p, and XY XY 12, YZ 2g, and XZ XY 4m, YZ 3m, and XZ XY 2c 1, YZ 6c, and XZ 81 Use the figures to determine whether each pair of segments is congruent. 13., 14., 15. W X, W Z 2 m 9 ft 12 yd Y Z 3 m 3 m 10 yd 5 ft 5 ft 5 m 12 yd X W Glencoe/cGraw-Hill 9 Glencoe Geometry
8 1-2 IO ractice Linear easure and recision ind the length of each line segment or object in. 1 2 cm ind the precision for each measurement meters inches millimeters 4 ind the measurement of each segment W X 18.4 cm 4.7 cm in in. W X 89.6 cm Y 100 cm ind the value of the variable and KL if K is between J and L. 9. JK 6r, KL 3r, and JL JK 2s, KL s 2, and JL 5s 10 Use the figures to determine whether each pair of segments is congruent. 11. U, W 12., 13. G, 2 ft 12.7 in. 5x G H 2 ft 3 ft 6x U W 3 ft 12.9 in. 14. Y Jorge used the figure at the right to make a pattern for a mosaic he plans to inlay on a tabletop. ame all of the congruent segments in the figure. Glencoe/cGraw-Hill 10 Glencoe Geometry
9 1-3 IO tudy Guide and Intervention istance and idpoints istance etween wo oints istance on a umber Line istance in the oordinate lane a b b a or a b ythagorean heorem: a 2 b 2 c 2 istance ormula: d (x x 2 1 ) 2 (y 2 y 1 ) 2 ( 2, 1) O y (1, 3) x (1, 1) xample 1 xample 2 ind ( 4) ind the distance between ( 2, 1) and (1, 3). ythagorean heorem () 2 () 2 () 2 () 2 (3) 2 (4) 2 () istance ormula d (x x 2 1 ) 2 (y 2 y 1 ) 2 (1 2)) ( 2 (3 ( 1)) 2 (3) 2 (4) xercises Use the number line to find each measure G G 6. G G Lesson 1-3 Use the ythagorean heorem to find the distance between each pair of points. 9. (0, 0), (6, 8) 10. ( 2, 3), (3, 15) 11. (1, 2), (9, 13) 12. ( 12, 2), ( 9, 6) Use the istance ormula to find the distance between each pair of points. 13. (0, 0), (15, 20) 14. O( 12, 0), ( 8, 3) 15. (11, 12), (6, 2) 16. ( 2, 10), ( 4, 3) Glencoe/cGraw-Hill 13 Glencoe Geometry
10 1-3 IO tudy Guide and Intervention (continued) istance and idpoints idpoint of a egment idpoint on a If the coordinates of the endpoints of a segment are a and b, umber Line then the coordinate of the midpoint of the segment is a. b 2 If a segment has endpoints with coordinates (x idpoint on a 1, y 1 ) and (x 2, y 2 ), oordinate lane then the coordinates of the midpoint of the segment are x 1 x, 2 y 1 y xample 1 ind the coordinate of the midpoint of he coordinates of and are 3 and 1. If is the midpoint of, then the coordinate of is or xample 2 is the midpoint of for ( 2, 4) and (4, 1). ind the coordinates of. x 2 x 1, y y , or (1, 2.5) xercises Use the number line to find the coordinate of the midpoint of each segment G G G G ind the coordinates of the midpoint of a segment having the given endpoints. 9. (0, 0), (12, 8) 10. ( 12, 8), (6, 12) 11. (11, 2), ( 9, 13) 12. ( 2, 6), ( 9, 3) 13. (10, 22), (9, 10) 14. ( 11, 2), ( 19, 6) Glencoe/cGraw-Hill 14 Glencoe Geometry
11 1-3 IO kills ractice istance and idpoints Use the number line to find each measure. J K L 1. L 2. JL K 4. Use the ythagorean heorem to find the distance between each pair of points y y G O x O x 7. K(2, 3), (4, 4) 8. ( 3, 1), ( 2, 3) Use the istance ormula to find the distance between each pair of points. 9. Y(2, 0), (2, 6) 10. W( 2, 2), (5, 2) 11. ( 7, 3), (5, 2) 12. ( 3, 1), (2, 6) Use the number line to find the coordinate of the midpoint of each segment Lesson ind the coordinates of the midpoint of a segment having the given endpoints. 17. (3, 1), U(5, 3) 18. J( 4, 2), (5, 2) ind the coordinates of the missing endpoint given that is the midpoint of. 19. (2, 0), (5, 2) 20. (5, 4), (6, 3) 21. (3, 9), ( 1, 5) Glencoe/cGraw-Hill 15 Glencoe Geometry
12 1-3 IO ractice istance and idpoints Use the number line to find each measure. 1. VW 2. V V U V W Use the ythagorean heorem to find the distance between each pair of points. 5. y 6. Z y O x O x Use the istance ormula to find the distance between each pair of points. 7. L( 7, 0), Y(5, 9) 8. U(1, 3), (4, 6) Use the number line to find the coordinate of the midpoint of each segment ind the coordinates of the midpoint of a segment having the given endpoints. 13. K( 9, 3), H(5, 7) 14. W( 12, 7), ( 8, 4) ind the coordinates of the missing endpoint given that is the midpoint of. 15. (5, 8), (4, 3) 16. (2, 9), ( 1, 6) 17. ( 3, 8), (1, 2) 18. I he coordinates of the vertices of a quadrilateral are ( 1, 3), (3, 3), (5, 1), and U( 2, 1). ind the perimeter of the quadrilateral. ound to the nearest tenth. Glencoe/cGraw-Hill 16 Glencoe Geometry
13 1-4 IO tudy Guide and Intervention ngle easure easure ngles If two noncollinear rays have a common endpoint, they form an angle. he rays are the sides of the angle. he common endpoint is the vertex. he angle at the right can be named as,,, or 1. right angle is an angle whose measure is 90. n acute angle has measure less than 90. n obtuse angle has measure greater than 90 but less than 180. xample 1 xample easure each angle and classify it as right, acute, or obtuse. 1 a. ame all angles that have as a vertex. hree angles are 1, 2, and 3. or other angles, use three letters to name them:,, and. b. ame the sides of 1., a. Using a protractor, m , so is an acute angle. b. Using a protractor, m , so is an obtuse angle. c. Using a protractor, m 90. is a right angle. xercises efer to the figure. 1. ame the vertex of ame the sides of. 3. Write another name for Lesson 1-4 easure each angle in the figure and classify it as right, acute, or obtuse Glencoe/cGraw-Hill 19 Glencoe Geometry
14 1-4 IO tudy Guide and Intervention (continued) ngle easure ongruent ngles ngles that have the same measure are congruent angles. ray that divides an angle into two congruent angles is called an angle bisector. In the figure, is the angle bisector of. oint lies in the interior of and. xample efer to the figure above. If m 2x 14 and m x 34, find x and find m. ince bisects,, or m m. 2x 14 x 34 m (2x 14) (x 34) 2x 14 x x 34 x x x x 20 xercises bisects, and and are opposite rays. 1. If m 60 and m 4x 14, find the value of x. 2. If m 3x 13 and m 6x 2, find m. and are opposite rays, bisects, and bisects. 3. If m 6x 4 and m 7x 2, find m If m 1 4x 10 and m 2 5x, find m If m 2 6y 2 and m 1 8y 14, find m. 6. Is a right angle? xplain. Glencoe/cGraw-Hill 20 Glencoe Geometry
15 1-4 IO kills ractice ngle easure or xercises 1 12, use the figure at the right. ame the vertex of each angle W U V ame the sides of each angle V 8. 1 Write another name for each angle W easure each angle and classify it as right, acute, or obtuse O O O LG In the figure, and are opposite rays, bisects, and bisects. 17. If m 4x 16 and m 6x 4, find m. L Lesson If m 7x 8 and m 5x 10, find m. Glencoe/cGraw-Hill 21 Glencoe Geometry
16 1-4 IO ractice ngle easure or xercises 1 10, use the figure at the right. ame the vertex of each angle ame the sides of each angle O O 8. O Write another name for each angle easure each angle and classify it as right, acute, or obtuse. V W 11. UZW 12. YZW U X 13. ZW 14. UZ Z Y LG In the figure, and are opposite rays, bisects, and G bisects. 15. If m 4x 15 and m 6x 5, find m. 16. If m G 9x 3 and m G 13x 9, find m G. G 17. I IG he diagram shows a sign used to warn drivers of a school zone or crossing. easure and classify each numbered angle. 2 1 Glencoe/cGraw-Hill 22 Glencoe Geometry
17 1-5 IO tudy Guide and Intervention ngle elationships airs of ngles djacent angles are angles in the same plane that have a common vertex and a common side, but no common interior points. Vertical angles are two nonadjacent angles formed by two intersecting lines. pair of adjacent angles whose noncommon sides are opposite rays is called a linear pair. xample Identify each pair of angles as adjacent angles, vertical angles, and/or as a linear pair. a. c. and U have a common vertex and a common side, but no common interior points. hey are adjacent angles. U and 5 are adjacent angles whose noncommon sides are opposite rays. he angles form a linear pair. xercises b. d. 1 and 3 are nonadjacent angles formed by two intersecting lines. hey are vertical angles. 2 and 4 are also vertical angles G and are two angles whose measures have a sum of 90. hey are complementary. and G are two angles whose measures have a sum of 180. hey are supplementary. Identify each pair of angles as adjacent, vertical, and/or as a linear pair. U 1. 1 and and 6 V and and 2 or xercises 5 7, refer to the figure at the right. 5. Identify two obtuse vertical angles. V 6. Identify two acute adjacent angles. U 7. Identify an angle supplementary to U. 8. ind the measures of two complementary angles if the difference in their measures is 18. Lesson 1-5 Glencoe/cGraw-Hill 25 Glencoe Geometry
18 1-5 IO tudy Guide and Intervention (continued) ngle elationships erpendicular Lines Lines, rays, and segments that form four right angles are perpendicular. he right angle symbol indicates that the lines are perpendicular. In the figure at the right, is perpendicular to, or. xample ind x so that Z Z. If Z Z, then m Z 90. m Z m Z m Z um of parts whole (9x 5) (3x 1) 90 ubstitution 12x 6 90 implify. 12x 84 x 7 ivide each side by 12. ubtract 6 from each side. (9x 5) (3x 1) Z xercises 1. ind x and y so that. 2. ind m. 5x (9y 18) x 3. m 3x 10, m x, and. ind x. 4. If m 7y 3 and m 3y 3, find y so that. 5. ind x, m, and m. 3x (8x 2) 6. ind y, m, and m W. (4y 5) W (2y 5) V Glencoe/cGraw-Hill 26 Glencoe Geometry
19 1-5 IO kills ractice ngle elationships or xercises 1 6, use the figure at the right and a protractor. 1. ame two acute vertical angles. K 2. ame two obtuse vertical angles. H G J 3. ame a linear pair. 4. ame two acute adjacent angles. 5. ame an angle complementary to KH. 6. ame an angle supplementary to KG. 7. ind the measures of an angle and its complement if one angle measures 18 degrees more than the other. 8. he measure of the supplement of an angle is 36 less than the measure of the angle. ind the measures of the angles. LG or xercises 9 10, use the figure at the right. 9. If m 8x 18, find x so that. 10. If m 3y 10 and m y, find y so that is a right angle. etermine whether each statement can be assumed from the figure. xplain. 11. WZU is a right angle. W V 12. YZU and UZV are supplementary. X Y Z U 13. VZU is adjacent to YZX. Lesson 1-5 Glencoe/cGraw-Hill 27 Glencoe Geometry
20 1-5 IO ractice ngle elationships or xercises 1 4, use the figure at the right and a protractor. 1. ame two obtuse vertical angles. 2. ame a linear pair whose vertex is. 3. ame an angle not adjacent to but complementary to G. G H 4. ame an angle adjacent and supplementary to. 5. wo angles are complementary. he measure of one angle is 21 more than twice the measure of the other angle. ind the measures of the angles. 6. If a supplement of an angle has a measure 78 less than the measure of the angle, what are the measures of the angles? LG or xercises 7 8, use the figure at the right. 7. If m G 5x 10, find x so that. 8. If m G 16x 4 and m G 2x 13, find x so that G is a right angle. G etermine whether each statement can be assumed from the figure. xplain. 9. O and O are complementary. O 10. and is a linear pair. 11. and are vertical angles. 12. arren sketched a map of the cross streets nearest to his home for his friend iguel. escribe two different angle relationships between the streets. eacon Olive ain Glencoe/cGraw-Hill 28 Glencoe Geometry
21 IO 1-6 tudy Guide and Intervention olygons olygons polygon is a closed figure formed by a finite number of coplanar line segments. he sides that have a common endpoint must be noncollinear and each side intersects exactly two other sides at their endpoints. polygon is named according to its number of sides. regular polygon has congruent sides and congruent angles. polygon can be concave or convex. xample ame each polygon by its number of sides. hen classify it as concave or convex and regular or irregular. a. b. I H L Lesson 1-6 c. G he polygon has 4 sides, so it is a quadrilateral. It is concave because part of or lies in the interior of the figure. ecause it is concave, it cannot have all its angles congruent and so it is irregular. d. J K he figure is not closed, so it is not a polygon. he polygon has 5 sides, so it is a pentagon. It is convex. ll sides are congruent and all angles are congruent, so it is a regular pentagon. he figure has 8 congruent sides and 8 congruent angles. It is convex and is a regular octagon. xercises ame each polygon by its number of sides. hen classify it as concave or convex and regular or irregular Glencoe/cGraw-Hill 31 Glencoe Geometry
22 1-6 IO tudy Guide and Intervention (continued) olygons erimeter he perimeter of a polygon is the sum of the lengths of all the sides of the polygon. here are special formulas for the perimeter of a square or a rectangle. xample Write an expression or formula for the perimeter of each polygon. ind the perimeter. a. 3 in. a 4 in. b c 5 in. a b c in. b. 5 cm s 5 cm s s 5 cm s 5 cm 4s 4(5) 20 cm c. 2 ft w 3 ft 2 2w 2(3) 2(2) 10 ft w xercises ind the perimeter of each figure cm 3 cm 5.5 ft 3.5 cm square yd 27 yd 12 yd 14 yd 24 yd 1 cm ind the length of each side of the polygon for the given perimeter x x x 2 x x rectangle 2x Glencoe/cGraw-Hill 32 Glencoe Geometry
23 IO 1-6 kills ractice olygons ame each polygon by its number of sides and then classify it as convex or concave and regular or irregular Lesson ind the perimeter of each figure yd yd 20 yd 40 yd 4 m 6 m 2 m 3 m 5 m 10 in. 2 in. 2 in. 2 in. 2 in. 2 in. 10 in. 2 in. OOI GOY ind the perimeter of each polygon. 10. triangle with vertices (3, 5), (3, 1), and (0, 1) 11. quadrilateral with vertices ( 3, 2), (1, 2), (1, 4), and ( 3, 4) 12. quadrilateral LO with vertices L( 1, 4), (3, 4), (2, 1), and O( 2, 1) LG ind the length of each side of the polygon for the given perimeter millimeters kilometers feet 4w 1 w Glencoe/cGraw-Hill 33 Glencoe Geometry
24 1-6 IO ractice olygons ame each polygon by its number of sides and then classify it as convex or concave and regular or irregular ind the perimeter of each figure mm mm 21 mi 33 mi 10 mm 18 mm 32 mi 2 cm 6 cm 14 cm 4 cm 6 cm 6 cm 14 cm 4 cm OOI GOY ind the perimeter of each polygon. 7. quadrilateral O with vertices O( 3, 2), (1, 5), (6, 4), and (5, 2) 8. pentagon UVW with vertices (0, 0), (3, 2), U(2, 5), V( 2, 5), and W( 3, 2) LG ind the length of each side of the polygon for the given perimeter inches centimeters feet 6n 8 n 3x 5 2x 3 x 9 2x 2 5x 4 WIG or xercises 12 13, use the following information. Jasmine plans to sew fringe around the scarf shown in the diagram. 12. How many inches of fringe does she need to purchase? 16 in. 4 in. 4 in. 16 in. 13. If Jasmine doubles the width of the scarf, how many inches of fringe will she need? Glencoe/cGraw-Hill 34 Glencoe Geometry
Geometry. Chapter 1 Resource Masters
Geometry hapter esource Masters eading to Learn Mathematics Vocabulary uilder This is an alphabetical list of the key vocabulary terms you will learn in hapter. s you study the chapter, complete each term
More information1-4. Study Guide and Intervention. Angle Measure
IO 1-4 tudy Guide and Intervention ngle easure easure ngles If two noncollinear rays have a common endpoint, they form an angle. he rays are the sides of the angle. he common endpoint is the vertex. he
More informationReading to Learn Mathematics
NME TE ERIO 1 Reading to Learn Mathematics Vocabulary uilder This is an alphabetical list of the key vocabulary terms you will learn in hapter 1. s you study the chapter, complete each term s definition
More information1-5. Skills Practice. Angle Relationships. Lesson 1-5. ALGEBRA For Exercises 9 10, use the figure at the right.
M IO kills ractice ngle elationships or xercises 6, use the figure at the right. ame an angle or angle pair that satisfies each condition.. ame two acute vertical angles. 2. ame two obtuse vertical angles.
More informationNAME DATE PERIOD. Study Guide and Intervention
NM T IO 1-5 tudy Guide and Intervention ngle elationships airs of ngles djacent angles are two angles that lie in the same plane and have a common vertex and a common side, but no common interior points.
More information1-4 Skills Practice. Angle Measure. Lesson 1-4. ALGEBRA In the figure, BA and BC are opposite
IO - kills ractice ngle easure or xercises 2, use the figure at the right. U ame the vertex of each angle. 5 3. 2. W 2 3. 2. 5 V ame the sides of each angle. 5. 6. 5 7. V 8. Write another name for each
More informationGeometry. Chapter 1 Resource Masters
Geometry hapter esource Masters onsumable Workbooks Many of the worksheets contained in the hapter esource Masters booklets are available as consumable workbooks. Study Guide and Intervention Workbook
More informationGeometry Reasons for Proofs Chapter 1
Geometry Reasons for Proofs Chapter 1 Lesson 1.1 Defined Terms: Undefined Terms: Point: Line: Plane: Space: Postulate 1: Postulate : terms that are explained using undefined and/or other defined terms
More informationMaintaining Mathematical Proficiency
Name Date Chapter 1 Maintaining Mathematical Proficiency Simplify the expression. 1. 3 + ( 1) = 2. 10 11 = 3. 6 + 8 = 4. 9 ( 1) = 5. 12 ( 8) = 6. 15 7 = + = 8. 5 ( 15) 7. 12 3 + = 9. 1 12 = Find the area
More informationSection 1-1 Points, Lines, and Planes
Section 1-1 Points, Lines, and Planes I CAN. Identify and model points, lines, and planes. Identify collinear and coplanar points and intersecting lines and planes in space. Undefined Term- Words, usually
More informationObjectives: (What You ll Learn) Identify and model points, lines, planes Identify collinear and coplanar points, intersecting lines and planes
Geometry Chapter 1 Outline: Points, Lines, Planes, & Angles A. 1-1 Points, Lines, and Planes (What You ll Learn) Identify and model points, lines, planes Identify collinear and coplanar points, intersecting
More information1.1 Practice A. Name Date. and plane X not intersecting. In Exercises 1 3, use the diagram. 1. Name two points. 2. Name two lines.
Name ate 1.1 Practice In xercises 1 3, use the diagram. 1. Name two points. 2. Name two lines. 3. Name the plane that contains point,, and. K In xercises 4 7, use the diagram. 4. ive one other name for
More informationNAME DATE PERIOD. Name each polygon by its number of sides and then classify it as convex or concave and regular or irregular.
Skills Practice Name each polygon by its number of sides and then classify it as convex or concave and regular or irregular. Lesson Find the perimeter or circumference of each figure. Round to the nearest
More informationName Date Period. 1.1 Understanding the Undefined Terms
Name Date Period Lesson Objective: 1.1 Understanding the Undefined Terms Naming Points, Lines, and Planes Point Line Plane Collinear: Coplanar: 1. Give 2 other names for PQ and plane R. 2. Name 3 points
More information1.1 Understanding the Undefined Terms
1.1 Understanding the Undefined Terms Undefined Terms There are three undefined terms in geometry, these words do not have a formal definition. The undefined terms are:,, and. Naming Points, Lines, and
More informationDear Parents/Students,
Dear Parents/Students, In the summer time, many necessary mathematical skills are lost due to the absence of daily exposure. The loss of skills may result in a lack of success and unnecessary frustration
More informationGeometry ~ Chapter 1 Capacity Matrix
Geometry ~ Chapter 1 Capacity Matrix Learning Targets 1. Drawing and labeling the Geometry Vocabulary 2. Using the distance and midpoint formula 3. Classifying triangles and polygons Section Required Assignments
More informationThere are two ways to name a line. What are the two ways?
Geometry: 1-1 Points, Lines and Planes What are the Undefined Terms? The Undefined Terms are: What is a Point? How is a point named? Example: What is a Line? A line is named two ways. What are the two
More informationGEOMETRY is the study of points in space
CHAPTER 5 Logic and Geometry SECTION 5-1 Elements of Geometry GEOMETRY is the study of points in space POINT indicates a specific location and is represented by a dot and a letter R S T LINE is a set of
More informationGeo - CH1 Practice Test
Geo - H1 Practice Test Multiple hoice Identify the choice that best completes the statement or answers the question. 1. Find the length of. a. = 7 c. = 7 b. = 9 d. = 8 2. Find the best sketch, drawing,
More informationGeometry - Chapter 1 - Corrective #1
Class: Date: Geometry - Chapter 1 - Corrective #1 Short Answer 1. Sketch a figure that shows two coplanar lines that do not intersect, but one of the lines is the intersection of two planes. 2. Name two
More information1-1. Points, Lines, and Planes. Lesson 1-1. What You ll Learn. Active Vocabulary
1-1 Points, Lines, and Planes What You ll Learn Scan the text in Lesson 1-1. Write two facts you learned about points, lines, and planes as you scanned the text. 1. Active Vocabulary 2. New Vocabulary
More informationGeometry Lesson 1-1: Identify Points, Lines, and Planes Name Hr Pg. 5 (1, 3-22, 25, 26)
Geometry Lesson 1-1: Identify Points, Lines, and Planes Name Hr Pg. 5 (1, 3-22, 25, 26) Learning Target: At the end of today s lesson we will be able to successfully name and sketch geometric figures.
More informationĚ PHDVXUH RI DQ DQJOH p. 17. Ě VLGHV RI DQ DQJOH p. 16 Ě FRQJUXHQW VHJPHQWV p. 10. Ě PLGSRLQW p. 11
Topic 1 eview TOPI VOULY Ě FXWH ULJKW WXVH VWULJKW JOHV p. 17 Ě FJUXHW JOHV p. 16 Ě PHVXUH I JOH p. 17 Ě VLGHV I JOH p. 16 Ě FJUXHW VHJPHWV p. 10 Ě PLGSLW p. 11 Ě VSFH p. 4 Ě GMFHW JOHV p. 22 Ě FVWUXFWL
More informationTest Review: Geometry I TEST DATE: ALL CLASSES TUESDAY OCTOBER 6
Test Review: Geometry I TEST DATE: ALL CLASSES TUESDAY OCTOBER 6 Notes to Study: Notes A1, B1, C1, D1, E1, F1, G1 Homework to Study: Assn. 1, 2, 3, 4, 5, 6, 7 Things it would be a good idea to know: 1)
More informationpine cone Ratio = 13:8 or 8:5
Chapter 10: Introducing Geometry 10.1 Basic Ideas of Geometry Geometry is everywhere o Road signs o Carpentry o Architecture o Interior design o Advertising o Art o Science Understanding and appreciating
More informationChapter 1: Essentials of Geometry
1.1 Identify Points, Lines, and Planes Chapter 1: Essentials of Geometry Point: Line: Collinear points: Coplanar points: Segment: Ray: Opposite rays: Example 1: Use the diagram at the right to answer the
More informationChapter 1. Essentials of Geometry
Chapter 1 Essentials of Geometry 1.1 Identify Points, Lines, and Planes Objective: Name and sketch geometric figures so you can use geometry terms in the real world. Essential Question: How do you name
More informationReteach. Understanding Points, Lines, and Planes. P point P
Name Date Class 1-1 Understanding Points, Lines, and Planes A point has no size. It is named using a capital letter. All the figures below contain points. line Figure Characteristics Diagram Words and
More informationGeometry 1-1. Non-collinear Points not on the same line. Need at least 3 points to be non-collinear since two points are always collinear
Name Geometry 1-1 Undefined terms terms which cannot be defined only described. Point, line, plane Point a location in space Line a series of points that extends indefinitely in opposite directions. It
More informationChapter 1-2 Points, Lines, and Planes
Chapter 1-2 Points, Lines, and Planes Undefined Terms: A point has no size but is often represented by a dot and usually named by a capital letter.. A A line extends in two directions without ending. Lines
More informationheptagon; not regular; hexagon; not regular; quadrilateral; convex concave regular; convex
10 1 Naming Polygons A polygon is a plane figure formed by a finite number of segments. In a convex polygon, all of the diagonals lie in the interior. A regular polygon is a convex polygon that is both
More informationDO NOT LOSE THIS REVIEW! You will not be given another copy.
Geometry Fall Semester Review 2011 Name: O NOT LOS THIS RVIW! You will not be given another copy. The answers will be posted on your teacher s website and on the classroom walls. lso, review the vocabulary
More informationLesson 1.1 Building Blocks of Geometry
Lesson 1.1 uilding locks of Geometry For xercises 1 7, complete each statement. S 3 cm. 1. The midpoint of Q is. N S Q. NQ. 3. nother name for NS is.. S is the of SQ. 5. is the midpoint of. 6. NS. 7. nother
More informationTerm: description named by notation (symbols) sketch an example. The intersection of two lines is a. Any determine a line.
Term: description named by notation (symbols) sketch an example point line plane Collinear points Examples: Non-collinear points Examples: Coplanar: Examples: Non-coplanar: Examples: The intersection of
More informationUnit 10 Study Guide: Plane Figures
Unit 10 Study Guide: Plane Figures *Be sure to watch all videos within each lesson* You can find geometric shapes in art. Whether determining the amount of leading or the amount of glass needed for a piece
More informationGeometry. Chapter 1 Points, Lines, Planes, and Angles
Geometry Chapter 1 Points, Lines, Planes, and Angles ***In order to get full credit for your assignments they must me done on time and you must SHOW ALL WORK. *** Algebraic Equations Review Keystone Vocabulary
More informationTerm Definition Figure
Notes LT 1.1 - Distinguish and apply basic terms of geometry (coplanar, collinear, bisectors, congruency, parallel, perpendicular, etc.) Term Definition Figure collinear on the same line (note: you do
More information1.1 Points, Lines, and Planes ASSIGNMENT Hour Date
1.1 Points, Lines, and Planes ASSIGNMENT Hour Date Refer to the figure at the right. 1. Name a line that contains point A. 2. What is another name for line m? 3. Name a point not on AC. 4. Name the intersection
More informationWriting Linear Equations
Writing Linear Equations Name: SHOW ALL WORK!!!!! For full credit, show all work on all problems! Write the slope-intercept form of the equation of each line. 1. 3x 2y = 16 2. 13x 11y = 12 3. 4x y = 1
More informationNAME DATE PER. GEOMETRY FALL SEMESTER REVIEW FIRST SIX WEEKS PART 1. A REVIEW OF ALGEBRA Find the correct answer for each of the following.
NAME ATE PER. GEOMETRY FALL SEMESTER REVIEW FIRST SIX WEEKS PART 1. A REVIEW OF ALGEBRA Find the correct answer for each of the following. 1. m = Solve for m : m 7 = -13 + m FIRST SIX-WEEKS REVIEW 2. x
More informationM2 GEOMETRY REVIEW FOR MIDTERM EXAM
M2 GEOMETRY REVIEW FOR MIDTERM EXAM #1-11: True or false? If false, replace the underlined word or phrase to make a true sentence. 1. Two lines are perpendicular if they intersect to form a right angle.
More information1) Draw line m that contains the points A and B. Name two other ways to name this line.
1) Draw line m that contains the points A and B. Name two other ways to name this line. 2) Find the next 3 terms in the sequence and describe the pattern in words. 1, 5, 9, 13,,, 3) Find the next 3 terms
More informationB. Section 1.1. Chapter 1 Review Booklet A. Vocabulary Match the vocabulary term with its definition. 3. A pair of opposite rays on line p.
A. Vocabulary Match the vocabulary term with its definition. Point Polygon Angle Sides Postulate Collinear Opposite Rays Vertical angles Coplanar Linear Pair Complementary Vertex Line Adjacent Plane Distance
More informationGeometry Semester 1 Final Exam Study Guide FCS, Mr. Garcia
Name Date Period This is your semester 1 exam review study guide. It is designed for you to do a portion each day until the day of the exam. You may use the following formula to calculate your semester
More informationDear Parents and Students,
Dear Parents and Students, Mathematics is a discipline that constantly builds on previous knowledge. Students entering Honors Geometry will be expected to recall and apply the material that they learned
More informationMoore Catholic High School Math Department
Moore Catholic High School Math Department Geometry Vocabulary The following is a list of terms and properties which are necessary for success in a Geometry class. You will be tested on these terms during
More informationPostulates, Theorems, and Corollaries. Chapter 1
Chapter 1 Post. 1-1-1 Through any two points there is exactly one line. Post. 1-1-2 Through any three noncollinear points there is exactly one plane containing them. Post. 1-1-3 If two points lie in a
More informationMath 3315: Geometry Vocabulary Review Human Dictionary: WORD BANK
Math 3315: Geometry Vocabulary Review Human Dictionary: WORD BANK [acute angle] [acute triangle] [adjacent interior angle] [alternate exterior angles] [alternate interior angles] [altitude] [angle] [angle_addition_postulate]
More informationLincoln Public Schools GEOMETRY REVIEW - Semester One CALCULATOR Revised 12/2007
Lincoln Public chools GOMY VIW - emester One LULO evised /007. escribe the lines in the sketch.. coplanar and intersecting. coplanar and nonintersecting. noncoplanar and intersecting. noncoplanar and nonintersecting.
More information1-1 Understanding Points, Lines, and Planes (pp. 6 11) Vocabulary EXERCISES
Vocabulary acute angle.................. 1 adjacent angles.............. 8 angle....................... 0 angle bisector............... 3 area........................ 36 base........................ 36
More informationSkills Practice Skills Practice for Lesson 3.1
Skills Practice Skills Practice for Lesson.1 Name ate onstellations Naming, Measuring, and lassifying ngles Vocabulary Write the term from the box that best completes each statement. point line segment
More informationBENCHMARK Name Points, Lines, Segments, and Rays. Name Date. A. Line Segments BENCHMARK 1
A. Line Segments (pp. 1 5) In geometry, the words point, line and plane are undefined terms. They do not have formal definitions but there is agreement about what they mean. Terms that can be described
More information(Current Re nweb Grade)x.90 + ( finalexam grade) x.10 = semester grade
2//2 5:7 PM Name ate Period This is your semester exam which is worth 0% of your semester grade. You can determine grade what-ifs by using the equation below. (urrent Re nweb Grade)x.90 + ( finalexam grade)
More information1. Revision Description Reflect and Review Teasers Answers Recall of basics of triangles, polygons etc. Review Following are few examples of polygons:
1. Revision Recall of basics of triangles, polygons etc. The minimum number of line segments required to form a polygon is 3. 1) Name the polygon formed with 4 line segments of equal length. 1) Square
More informationMath 7, Unit 08: Geometric Figures Notes
Math 7, Unit 08: Geometric Figures Notes Points, Lines and Planes; Line Segments and Rays s we begin any new topic, we have to familiarize ourselves with the language and notation to be successful. My
More informationEssential Question How can you describe angle pair relationships and use these descriptions to find angle measures?
1.6 escribing Pairs of ngles OMMON OR Learning Standard HSG-O..1 ssential Question How can you describe angle pair relationships and use these descriptions to find angle measures? Finding ngle Measures
More informationGeometry. Geometry is the study of shapes and sizes. The next few pages will review some basic geometry facts. Enjoy the short lesson on geometry.
Geometry Introduction: We live in a world of shapes and figures. Objects around us have length, width and height. They also occupy space. On the job, many times people make decision about what they know
More informationPre-AP Geometry Chapter 1 TEST Review Important Vocabulary
1 Pre-AP Geometry Chapter 1 TEST Review Important Vocabulary Space Undefined Line segment Congruent segments Geometry Euclid Conditional Converse Postulate Theorem Converse Hypothesis Conclusion Venn Congruent
More informationUnit 1: Foundations of Geometry Section 1: Points, Lines & Planes. The most basic figures in geometry are.
Unit 1: Foundations of Geometry Section 1: Points, Lines & Planes The most basic figures in geometry are. 1 Intersections: Lines Planes Ex #1 2 1a. Name four coplanar points. 1b. Name three lines. 2.Use
More informationPLANE GEOMETRY SKILL BUILDER ELEVEN
PLANE GEOMETRY SKILL BUILDER ELEVEN Lines, Segments, and Rays The following examples should help you distinguish between lines, segments, and rays. The three undefined terms in geometry are point, line,
More informationPoints, Lines, and Planes 1.1
Points, Lines, and Planes 1.1 Point a location ex. write as: Line made up of points and has no thickness or width. ex. c write as:, line c ollinear points on the same line. Noncollinear points not on the
More informationMrs. Daniel s Geometry Vocab List
Mrs. Daniel s Geometry Vocab List Geometry Definition: a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. Refectional Symmetry Definition:
More informationPoints, Lines, Planes, & Angles
Points, Lines, Planes, and ngles Points, Lines, Planes, & ngles www.njctl.org Table of ontents Points, Lines, & Planes Line Segments Simplifying Perfect Square Radical Expressions Rational & Irrational
More informationMath 7, Unit 8: Geometric Figures Notes
Math 7, Unit 8: Geometric Figures Notes Points, Lines and Planes; Line Segments and Rays s we begin any new topic, we have to familiarize ourselves with the language and notation to be successful. My guess
More informationMath 6, Unit 8 Notes: Geometric Relationships
Math 6, Unit 8 Notes: Geometric Relationships Points, Lines and Planes; Line Segments and Rays As we begin any new topic, we have to familiarize ourselves with the language and notation to be successful.
More informationIsosceles Triangles. leg. base
6 4 What ou ll Learn ou ll learn to identif and use properties of isosceles triangles. Isosceles riangles ecall from Lesson 5 that an isosceles triangle has at least two congruent sides. he congruent sides
More informationParallel Lines: Two lines in the same plane are parallel if they do not intersect or are the same.
Section 2.3: Lines and Angles Plane: infinitely large flat surface Line: extends infinitely in two directions Collinear Points: points that lie on the same line. Parallel Lines: Two lines in the same plane
More informationReview Test 1 Chapters 1 & 2 and Appendix L
Math 61 pring 2009 Review Test 1 hapters 1 & 2 and ppendix L www.timetodare.com 1 To prepare for the test, learn all definitions, be familiar with all theorems and postulates, study all exercises and theorems
More informationPolygons. 5 sides 5 angles. pentagon. Name
Lesson 11.1 Reteach Polygons A polygon is a closed plane figure formed by three or more line segments that meet at points called vertices. You can classify a polygon by the number of sides and the number
More informationReview Test 1 Chapters 1 & 2 and Appendix L
ath 61 pring 2007 Review Test 1 hapters 1 & 2 and Appendix L 1 www.timetodare.com To prepare for the test, learn all definitions, be familiar with all theorems and postulates and study the following problems.
More informationObjective- the students will be able to use undefined terms and definitions to work with points, lines and planes. Undefined Terms
Unit 1 asics of Geometry Objective- the students will be able to use undefined terms and definitions to work with points, lines and planes. Undefined Terms 1. Point has no dimension, geometrically looks
More informationUnit 2: Triangles and Quadrilaterals Lesson 2.1 Apply Triangle Sum Properties Lesson 4.1 from textbook
Unit 2: Triangles and Quadrilaterals Lesson 2.1 pply Triangle Sum Properties Lesson 4.1 from textbook Objectives Classify angles by their sides as equilateral, isosceles, or scalene. Classify triangles
More information8.1 Practice A. Name Date. Then find the area of XYZ. to the perimeter of XYZ.
ame ate.1 ractice In ercises 1 and 2, find the scale factor. hen list all pairs of congruent angles and write the ratios of the corresponding side lengths in a statement of proportionality. 1. 2. GH 13
More informationGeometry Chapter 1 Basics of Geometry
Geometry Chapter 1 asics of Geometry ssign Section Pages Problems 1 1.1 Patterns and Inductive Reasoning 6-9 13-23o, 25, 34-37, 39, 47, 48 2 ctivity!!! 3 1.2 Points, Lines, and Planes 13-16 9-47odd, 55-59odd
More informationGeometry Definitions and Theorems. Chapter 9. Definitions and Important Terms & Facts
Geometry Definitions and Theorems Chapter 9 Definitions and Important Terms & Facts A circle is the set of points in a plane at a given distance from a given point in that plane. The given point is the
More informationLines Plane A flat surface that has no thickness and extends forever.
Lines Plane A flat surface that has no thickness and extends forever. Point an exact location Line a straight path that has no thickness and extends forever in opposite directions Ray Part of a line that
More informationIntroduction to Geometry
Introduction to Geometry Building Blocks of Geometry I. Three building blocks of geometry: points, lines, and planes. 1. A point is the most basic building block of geometry. It has no size. It only has
More informationSummer Dear Geometry Students and Parents:
Summer 2018 Dear Geometry Students and Parents: Welcome to Geometry! For the 2018-2019 school year, we would like to focus your attention to the prerequisite skills and concepts for Geometry. In order
More informationMrs. Daniel s Geometry Vocab List
Mrs. Daniel s Geometry Vocab List Geometry Definition: a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. Reflectional Symmetry
More informationGeometry Definitions, Postulates, and Theorems. Chapter 4: Congruent Triangles. Section 4.1: Apply Triangle Sum Properties
Geometry efinitions, Postulates, and Theorems Key hapter 4: ongruent Triangles Section 4.1: pply Triangle Sum Properties Standards: 12.0 Students find and use measures of sides and of interior and exterior
More informationEssential Question What are some properties of trapezoids and kites? Recall the types of quadrilaterals shown below.
7.5 Properties of Trapezoids and ites ssential Question What are some properties of trapezoids and kites? ecall the types of quadrilaterals shown below. Trapezoid Isosceles Trapezoid ite PV I OVI PO To
More informationAngle Unit Definitions
ngle Unit Definitions Name lock Date Term Definition Notes Sketch D djacent ngles Two coplanar angles with a coon side, a coon vertex, and no coon interior points. Must be named with 3 letters OR numbers
More informationCHAPTER 5 RELATIONSHIPS WITHIN TRIANGLES
HPTR 5 RLTIONSHIPS WITHIN TRINGLS In this chapter we address three ig IS: 1) Using properties of special segments in triangles ) Using triangle inequalities to determine what triangles are possible 3)
More informationAngle Bisectors of Triangles
6 What You ll Learn You ll learn to identify and use angle bisectors in triangles. ngle isectors of Triangles ecall that the bisector of an angle is a ray that separates the angle into two congruent angles.
More informationGeometry Basics of Geometry Precise Definitions Unit CO.1 OBJECTIVE #: G.CO.1
OBJECTIVE #: G.CO.1 OBJECTIVE Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance
More informationBisectors, Medians, and Altitudes
isectors, Medians, and ltitudes Identify and use perpendicular bisectors and angle bisectors in triangles. Identify and use medians and altitudes in triangles. Vocabulary perpendicular bisector concurrent
More informationCST Geometry Practice Problems
ST Geometry Practice Problems. Which of the following best describes deductive reasoning? using logic to draw conclusions based on accepted statements accepting the meaning of a term without definition
More information1.1 Building Blocks of Geometry
1.1 uilding locks of Geometry Name Definition Picture Short Rorm Point A location in space The point P Line An infinite number of points extending in two directions. A line only has length. T M TM Ray
More informationGeometry. Chapter 4 Resource Masters
Geometry hapter 4 esource Masters NME E PEI 4 eading to Learn Mathematics Vocabulary uilder his is an alphabetical list of the key vocabulary terms you will learn in hapter 4. s you study the chapter,
More information1. A statement is a set of words and/or symbols that collectively make a claim that can be classified as true or false.
Chapter 1 Line and Angle Relationships 1.1 Sets, Statements and Reasoning Definitions 1. A statement is a set of words and/or symbols that collectively make a claim that can be classified as true or false.
More informationBasics of Geometry Unit 1 - Notes. Objective- the students will be able to use undefined terms and definitions to work with points, lines and planes.
asics of Geometry Unit 1 - Notes Objective- the students will be able to use undefined terms and definitions to work with points, lines and planes. Undefined Terms 1. Point has no dimension, geometrically
More information15. K is the midpoint of segment JL, JL = 4x - 2, and JK = 7. Find x, the length of KL, and JL. 8. two lines that do not intersect
Name: Period Date Pre-AP Geometry Fall Semester Exam REVIEW *Chapter 1.1 Points Lines Planes Use the figure to name each of the following: 1. three non-collinear points 2. one line in three different ways
More information1.3 Points, Lines, and Planes
1.3 oints, ines, and lanes oal Use postulates and undefined terms. ey Words undefined term point, line, plane postulate collinear, coplanar segment ray he legs of the tripod touch the table at three points.
More informationEssential Question What are the properties of parallelograms?
7. roperties of arallelograms ssential uestion What are the properties of parallelograms? iscovering roperties of arallelograms Work with a partner. Use dynamic geometry software. a. onstruct any parallelogram
More informationReporting Category 3. Geometry and Measurement BINGO
Reporting Category 3 Geometry and Measurement BINGO names an exact location in space, named by a capital letter Has NO width, length, or depth. 2 a straight path with 2 endpoints, has a definite beginning
More informationUnit 3. Chapter 1. Foundations of Geometry. Name. Hour
Unit 3 Chapter 1 Foundations of Geometry Name Hour 1 Geometry Unit 3 Foundations of Geometry Chapter 1 Monday October 1 Tuesday October 2 1.1 Understanding Points, Lines, & Planes 1.2 Linear Measure DHQ
More informationGeometry Chapter 1 TEST * Required
Geometry Chapter 1 TEST * Required Vocabulary Match each word with the correct definition or description. 1. Plane * A flat surface extending indefinitely The two rays that from an angle Exactly one of
More informationNORTH HAVEN HIGH SCHOOL. Applied Geometry (Level 1) Summer Assignment 2017
NORTH HAVEN HIGH SCHOOL 221 Elm Street North Haven, CT 06473 June 2017 Applied Geometry (Level 1) Summer Assignment 2017 Dear Parents, Guardians, and Students, The Geometry curriculum builds on geometry
More informationa triangle with all acute angles acute triangle angles that share a common side and vertex adjacent angles alternate exterior angles
acute triangle a triangle with all acute angles adjacent angles angles that share a common side and vertex alternate exterior angles two non-adjacent exterior angles on opposite sides of the transversal;
More information