1.1 Practice A. Name Date. and plane X not intersecting. In Exercises 1 3, use the diagram. 1. Name two points. 2. Name two lines.

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1 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 N. 5. Name three points that are collinear. 6. Name three points that are coplanar. V W N P s 7. Name a point that is not coplanar with points N, P, and. In xercises 8, sketch the figure described. 8. plane and line c intersecting at all points on line c 9. and H. line and plane X not intersecting In xercises 11 14, use the diagram. 11. Name a point that is coplanar with points,, and. H 12. Name the intersection of plane H and plane. 13. Name a point that is collinear with H. L 14. Name a point that is not coplanar with points,, and. 15. What geometric terms are modeled by the iffel ower? opyright ig Ideas Learning, LL ll rights reserved. eometry 5

2 Name ate 1.1 Practice In xercises 1 4, use the diagram. 1. Name three points. 2. Name two lines. 3. Name all points in plane H. 4. Name the plane that contains points,, and. H In xercises 5 8, use the diagram. 5. Name one pair of opposite rays. 6. Name two points that are collinear with point. 7. Name the point of intersection of line with plane. 8. Name a point that is not coplanar with plane. In xercises 9 11, sketch the figure described. 9. plane and line intersecting at point. plane and plane N not intersecting 11. lines a, b, and c intersecting at three points 12. tripod can be used to level a camera. What geometric figure is modeled by the intersection of a tripod to the ground? xplain. In xercises 13 and 14, graph the inequality on a number line. ell whether the graph is a segment, a ray, a point, or a line. 13. x < x < What is the maximum number of times two planes can intersect? What is the minimum number of times they can intersect? 6 eometry opyright ig Ideas Learning, LL ll rights reserved.

3 Name ate 1.2 Practice In xercises 1 and 2, use a ruler to measure the length of the segment to the nearest eighth of an inch In xercises 3 5, plot the points in a coordinate plane. hen determine whether and UV are congruent. 3. ( 1, 2 ), ( 1, 1 ), U( 3, 5 ), V( 3, 2) 4. ( 1, 1 ), ( 1, 1 ), U( 3, 4 ), V( 5, 4) 5. ( 1, 3 ), ( 1, 3 ), U( 3, 2 ), V( 3, 2) In xercises 6 8, find K K 2 6 K L 12 L 14 L 3 K 9. escribe and correct the error in finding the length of. in man is 76 inches tall. he length from his head to his shoulders is 14 inches, and the length from his waist to his shoulders is 30 inches. What is the length from his feet to his waist? In xercises 11 13, determine whether the statement is true or false. xplain your reasoning. 11. is between and. 12. is between and. 13. is between and. eometry opyright ig Ideas Learning, LL ll rights reserved.

4 Name ate 1.2 Practice In xercises 1 and 2, use a ruler to measure the length of the segment to the nearest eighth of an inch In xercises 3 and 4, plot the points in a coordinate plane. hen determine whether and are congruent. 3. ( 7, 1 ), ( 4, 1 ), ( 3, 5 ), ( 3, 2) 4. ( 1, 1 ), ( 1, 1 ), ( 3, 4 ), ( 5, 4) In xercises 5 7, find R U 6 U he 2014 Winter Olympic ames were held in ochi, Russia. he distance between Washington, and Rome, Italy is about 4480 miles. he distance between Washington, and ochi, Russia is about 5500 miles. What is the distance between Rome, Italy and ochi, Russia? ochi, Russia Washington, Rome, Italy In xercises 9 and, point is between and on. Use the information to write an equation in terms of x. hen solve the equation and find,, and. 9. = x = 12 = x = 8x + 5 = 5x 9 = You participate in a 150-mile bicycle trip from adison, Wisconsin to hicago, Illinois. On the first day, you bike 46.8 miles. On the second day, you bike 51.4 miles. How many miles do you bike on the third day? Which day did you bike the most miles? opyright ig Ideas Learning, LL ll rights reserved. eometry 11

5 Name ate 1.3 Practice In xercises 1 and 2, identify the segment bisector of. hen find. 1. d L 5.5 In xercises 3 and 4, identify the segment bisector of. hen find x x 2 R 2x + 3 4x 7 In xercises 5 and 6, copy the segment and construct a segment bisector by paper folding. hen label the midpoint X Y In xercises 7 and 8, the endpoints of JK are given. ind the coordinates of the midpoint. 7. J( 3, 2 ) and K( 9, 2) 8. J( 1, 3 ) and K ( 7, 5) In xercises 9 and, the midpoint and one endpoint of are given. ind the coordinates of the other endpoint. 9. ( 2, 5 ) and ( 2, 3). ( 4, 4 ) and ( 1, 1 ) In xercises 11 and 12, find the distance between the two points. 11. Q( 5, 6 ) and P ( 1, 3) 12. ( 2, 5 ) and H( 4, 1) 13. square has a side length of 4 centimeters. What is the length of the diagonal of the square? What is the length from the corner to the center of the square? xplain. 14. uring a soccer game, Player is 87 feet from the goal but chooses to pass the ball to Player who is 63 feet away from Player. How far away is Player from the goal? Player 63 ft 87 ft Player oal opyright ig Ideas Learning, LL ll rights reserved. eometry 15

6 Name ate 1.3 Practice In xercises 1 and 2, identify the bisector of. hen find. 1. W x 6 x + 8 opy the segment and construct a segment bisector by paper folding. hen label the midpoint. 3. In xercises 4 and 5, the endpoints of LN are given. ind the coordinates of the midpoint. 4. L( 2, 1 ) and N ( 2, 13) 5. L( 6, 0 ) and N( 6, 6) In xercises 6 and 7, the midpoint and one endpoint of are given. ind the coordinates of the other endpoint. 6. ( 1, 2 ) and ( 1, 4) 7. ( 3, 7 ) and ( 1, 1) In xercises 8 and 9, find the distance between the two points. 8. ( 1, 7 ) and ( 4, 6) 9. ( 1, 5 ) and H( 3, 8). Your friend draws a square and one diagonal connecting its opposite vertices. Your friend believes that the diagonal is the same length as one side of the square. o you agree? xplain your reasoning. 11. Is it possible for a segment to have more than one bisector? xplain your reasoning. 12. You walk 2 miles from your house to the park and 4.5 miles from the park to the lake. hen you return home along a straight path from the lake. How many miles do you walk from the lake back to your house? What is the total distance you walk? Park 4.5 mi 2 mi House Lake 16 eometry opyright ig Ideas Learning, LL ll rights reserved.

7 Name ate 1.4 Practice In xercises 1 and 2, classify the polygon by the number of sides. ell whether it is concave or convex ind the perimeter of quadrilateral PQR with the vertices P( 2, 4 ), Q ( 2, 3 ), R( 2, 2 ), and ( 2, 3 ). In xercises 4 and 5, find the area of the polygon with the given vertices. 4. ( 0, 2 ), U( 3, 5 ), V( 3, 5) 5. ( 3, 3 ), ( 3, 1 ), ( 4, 1 ), ( 4, 3) In xercises 6, use the diagram. 6. ind the perimeter of square. 7. ind the perimeter of. y (4, 4) (0, 4) 4 ( 4, 0) (6, 4) 2 8. ind the area of square. 9. ind the area of.. ind the area of pentagon (4, 0) (0, 4) x 11. rectangle has vertices ( 1, 4, ) ( 3, 4, ) and ( 3, 3. ) ind the remaining vertex of the rectangle. What is the area of the rectangle? 12. You are installing a fence around your yard. In the figure, your yard is rectangle. ach unit in the coordinate plane represents feet. y 12 (1, 13) (7, 13) a. What is the perimeter of your entire yard? b. You consider only installing a fence around your backyard represented by rectangle. What is the perimeter of your backyard? c. he cost of fencing is $50 for each 6-foot section. How much do you save by only installing a fence in the backyard? 8 (1, 7) (7, 7) (7, 1) (1, 1) x 20 eometry opyright ig Ideas Learning, LL ll rights reserved.

8 Name ate 1.4 Practice In xercises 1 and 2, classify the polygon by the number of sides. ell whether it is convex or concave ind the perimeter of quadrilateral with vertices ( ) ( ) ( 5, 3, ) and ( 4, 2. ) 2, 2, 1, 3, In xercises 4 and 5, find the area of the polygon with the given vertices. 4. P( 1, 1, ) Q( 2, 1, ) R( 1, 4) 5. ( 3, 7 ), ( 5, 7 ), ( 3, 7 ), ( 5, 7) In xercises 6, use the diagram. 6. ind the perimeter of. 7. ind the perimeter of quadrilateral. ( 1, 5) ( 4, 3) 4 2 y (2, 3) 8. ind the area of. 9. ind the area of quadrilateral. 2 ( 2, 3) ( 4, 3) 2 4 x (4, 3). ind the area of pentagon. 11. You are buying tile for your bathroom floor and baseboards for your bathroom walls. In the figure, the entire polygon represents the layout of the floor. ach unit in the coordinate plane represents 1 foot. a. ind the area of the floor. b. ind the perimeter of the floor. c. he cost of the baseboard is $2 per foot. he cost of the tile is $2.50 per square foot. ind the total cost to buy tile and baseboards for your bathroom. y (0, ) (, ) 8 (3, 7) H(0, 7) 6 (8, 7) (, 7) 4 2 (3, 0) (8, 0) x 12. You and your friend go for a walk around town. You walk 0.8 mile east and then 1.5 miles south. You then return to where you started. How far do you travel during your entire walk? opyright ig Ideas Learning, LL ll rights reserved. eometry 21

9 0 180 Name ate 1.5 Practice 1. Write three names for the angle. 2. Name three different angles in the diagram. X P R Y Z 3. ind the angle measure of O. hen classify the angle. Q O In xercises 4 7, m = 92 and m = Identify the angles congruent to. 5. Identify the angles congruent to. 6. ind m I. 7. ind m H. In xercises 8 and 9, find the indicated angle measure. 8. ind m. 9. ind x. H I (2x 18) (4x) H. In the erris wheel, the measure of is and the measure of is 70. a. Name an example of each of the four types of angles according to their measures in the diagram. b. How many angles are congruent to? c. What is the measure of? d. What is the measure of? opyright ig Ideas Learning, LL ll rights reserved. eometry 25

10 0 180 Name ate 1.5 Practice In xercises 1 4, find the angle measure. hen classify the angle. 1. m O 2. m O 3. m O m O 170 O In xercises 5 8, find the indicated angle measure. 5. m = 130. ind m H. 6. m PR = 98. ind m QR. H P Q 86 (3x 8) R (2x + 6) 7. m JN = 3. ind m JNK. 8. ind m WXZ. N J Z W L K (7x ) Y (2x + 1) X 9. Your friend claims it is possible for a straight angle to consist of three acute angles. Is your friend correct? xplain your reasoning.. In the suspension bridge, m = 90, m = 29, m = 61, and bisects. a. Name an example of an acute angle, right angle, and straight angle according to their angle measures. b. Which angle is congruent to? c. What is the measure of? d. What is the measure of? 26 eometry opyright ig Ideas Learning, LL ll rights reserved.

11 Name ate 1.6 Practice In xercises 1 3, use the figures. 1. Name a pair of adjacent complementary angles. 2. Name a pair of nonadjacent complementary angles. 3. Name a pair of nonadjacent supplementary angles. In xercises 4 and 5, find the angle measure is a complement of 2, and m 2 = 36. ind m is a supplement of 4, and m 4 = 75. ind m H J In xercises 6 and 7, find the measure of each angle. 6. WXY and YXZ are supplementary angles, m WXY = ( 6x + 59 ), and ( x ) m YXZ = and are complementary angles, m = ( 3x + 6 ), and ( x ) m = In xercises 8, use the figure. 8. Identify the linear pairs that include re 3 and 5 vertical angles? xplain your reasoning.. re 2 and 4 vertical angles? xplain your reasoning In xercises 11 13, write and solve an algebraic equation to find the measure of each angle based on the given description. 11. wo angles form a linear pair. he measure of one angle is 24 more than the measure of the other angle. 12. he measure of an angle is three times the measurement of its complement. 13. he measure of one angle is 15 less than half the measurement of its supplement. 14. he figure shows the design on an outdoor fence. a. Name a pair of adjacent supplementary angles. b. Name a pair of nonadjacent supplementary angles. c. Identify the linear pairs that include 5. d. ind m 3. xplain your reasoning eometry opyright ig Ideas Learning, LL ll rights reserved.

12 Name ate 1.6 Practice In xercises 1 3, use the figures. 1. Name a pair of adjacent complementary angles. 2. Name a pair of nonadjacent complementary angles. 3. Name a pair of nonadjacent supplementary angles H J 22 K In xercises 4 and 5, find the angle measure is a complement of 2, and m 2 = 71. ind m is a supplement of 4, and m 4 = ind m 3. In xercises 6 and 7, find the measure of each angle. 6. and are supplementary angles, m = 7x and m = 8 x. 7. WXY and YXZ are complementary angles, m WXY = ( 2x + 5 ), and m YXZ ( x ) = 8 5. In xercises 8 11, use the figure. 8. Identify the linear pair(s) that include Identify the linear pair(s) that include 8.. re 6 and 8 vertical angles? xplain your reasoning. 11. re 7 and 9 vertical angles? xplain your reasoning In xercises 12 14, write and solve an algebraic equation to find the measure of each angle based on the given description. 12. he measure of an angle is 9 more than twice its complement. 13. wo angles form a linear pair. he measure of one angle is four times the measure of the other angle. 14. wo angles form a linear pair. he measure of one angle is 51 more than 1 2 the measure of the other angle. In xercises 15 and 16, tell whether the statement is always, sometimes, or never true. xplain your reasoning. 15. he sum of the measures of a linear pair of angles is he sum of the measures of a pair of vertical angles is 180. opyright ig Ideas Learning, LL ll rights reserved. eometry 31

Objectives: (What You ll Learn) Identify and model points, lines, planes Identify collinear and coplanar points, intersecting lines and planes

Objectives: (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