Day 1: Geometry Terms & Diagrams CC Geometry Module 1

Transcription

1 Name ate ay 1: Geometry Terms & iagrams Geometry Module 1 For #1-3: Identify each of the following diagrams with the correct geometry term. #1-3 Vocab. ank Line Segment Line Ray Explain why it is possible to determine the measure (or length) of line segment but not possible to talk about the measure (or length) of line or ray. For #5-7: Identify each of the following PIRS OF LINES with the correct geometry term. #5-7 Vocab. ank Intersecting Lines and Parallel Lines Perpendicular Lines E For #8-10: Identify each of the following NGLES with the correct geometry term. #8-10 Vocab. ank Right ngle cute ngle Obtuse ngle

2 For #11-13: Identify each of the following TRINGLES with the correct geometry term. #11-13 Vocab. ank Right Triangle Isosceles Triangle Equilateral Triangle For #14-17: Identify each of the following QURILTERLS with the correct geometry term. #14-17 Vocab. ank Parallelogram Rectangle Rhombus Square E E E E For #18-21: Identify each of the following POLYGONS with the correct geometry term. #18-21 Vocab. ank ecagon Octagon Pentagon Hexagon For #22-25: Identify each of the following TRNSFORMTION with the correct geometry term. #22-25 Vocab. ank Translation ilation Reflection Rotation

3 Name: ay 1and2 LabLesson: opying Segments & Triangles and Triangle Notation ate: Geometry (M1) Example 1: opying a Segment with your ompass (a) Using your compass, place the pointer at Point and extend the slider until reaches Point. Your compass now has the measure of. (b) Place your pointer at, and then create the arc using your compass. The intersection is the same radii, thus the same distance as. You have copied the length. Practice - NYTS (Now You Try Some) 1.opy the segment. ' 2. reate the length 3 ' 3. Given &. EF Use the copy segment construction to create a segment that is the length of + EF on the horizontal line below. 3

4 4. Given,,& EF, use the copy segment construction to create a triangle with the longest side lying on the horizontal line shown below. E F 5. Given, construct a copy of it,. ' 6. Match the sides and angles described below with the correct notation in the below triangle diagram. 1. The side that measures 8 cm. 2. The side that measures 9.5 cm. 3. The side that measures 14 cm. 4. The angle measuring 82 o. 5. The angle measuring 55 o. 6. The angle measuring 43 o. H. HT E. I Notation. < HT. < HT F. < TH 7. Match the sides and angles described below with the correct notation in the below triangle diagram. 1. The side with a single hash mark. 2. The side with 2 hash marks. 3. The side with 3 hash marks. 4. The right angle marked with a small square. 5. The angle marked with a single arc. 6. The angle marked with 2 arcs.. JK. IK Notation. < IJK. < JKI E. JI F. < JIK 4

5 Name: ay 2: onstruct an Equilateral Triangle ate: Geometry (M1L1&2) Opening Exercise: an and rad are in the park playing catch. Larry joins them, and the boys want to stand so that the distance between any two of them is the same. Where do they stand? How could they figure this out the most accurately? Term efinition iagram Line Segment part of a line with 2. (can be measured) Ray part of a line with 1 and extending in one direction. (cannot be measured) ngle figure formed by 2 with a common (vertex). (measured in ) Equilateral Triangle triangle with congruent sides and congruent angles. Geometric onstructions raw shapes, angles or lines accurately. These geometric constructions use only, (i.e. ruler) and a. Using only our compass and straightedge we can create a variety of triangles. One of the golden rules of construction is to always leave your construction marks. Example 2: Equilateral Triangle onstruction (a)using your compass, place the pointer at Point and extend it until reaches Point. (b) reate an arc (1/4 circle either above or below ). (c) Without changing your compass measurement, place your point at (d)the two arcs will intersect. Label the point and connect to points and. 5

6 Example 3: a. Using a compass, straightedge, and. [Leave all construction marks.] below, construct an equilateral triangle with all sides congruent to b. etermine the measure of each angle of Δ. Explain your answer. c. If side = 7 cm, what is the length of sides and? Practice NYTS (Now You Try Some) 1. onstruct equilateral triangles using the segments shown as one of the three equal sides. Leave all construction marks. a) b) 6

7 Example 4: is shown below. etermine if the triangle shown below is an equilateral triangle. Justify your answer. Example 5: Margie has three cats. She has heard that cats in a room position themselves at equal distances from one another and wants to test that theory. Margie notices that Simon, her tabby cat, is in the center of her bed (at S), while JoJo, her Siamese, is lying on her desk chair (at J). If the theory is true, where will she find Mack, her calico cat? Use the scale drawing of Margie s room shown below, together with (only) a compass and straightedge. Place an M where Mack will be if the theory is true. Practice - NYTS (Now You Try Some) 1. onstruct equilateral XYZ with all sides the same length as segment YZ shown below. 7

8 2. Which diagram shows the construction of an equilateral triangle? (1) (2) (3) (4) 3. On the ray drawn below, using a compass and straightedge, construct an equilateral triangle with a vertex at R. The length of a side of the triangle must be equal to a length of the diagonal of rectangle. (HINT: Start by placing pointer of compass on and open slider to, then move pointer to R and begin). 4. uring today s lesson we saw two different scenarios where we used the construction of an equilateral triangle to help determine a needed location (i.e., the friends playing catch in the park and the sitting cats). an you think of another scenario where the construction of an equilateral triangle might be useful? 8

9 hallenge Questions 1. onstruct THREE equilateral triangles, where the first and second triangles share a common side, and the second and third triangles share a common side. 2. Using a compass & ruler, construct a regular hexagon (6-sided shape consisting of 6 equilateral triangles). 9

10 Name: ate: ay 3: isect an ngle Geometry (M1 L3) Opening Exercise: a) Using a compass and straightedge, on the diagram below of with as one side and label the third vertex T. [Leave all construction marks.], construct an equilateral triangle b) Explain what you know about the length sides and the measures of the angles ofδrst Term efinition Symbol/Notation ngle isector ray that cuts an angle in. (Two angles) rc part of the of a circle. Types of ngles cute n angle that measures than 90 o Obtuse Straight Right n angle that measures than 90 o and than 180 o n angle that measures exactly n angle that measures exactly

11 Example 1: Given four possible correct names for the given angle isecting an ngle onstruction (a) Given an angle. (b) reate an arc of any size, such that it intersects both rays of the angle. Label those points and. (c) Leaving the compass the same measurement, place your pointer on point and create an arc in the interior of the angle. Video Example 1: onstruct the angle bisector for each angle below. (d) o the same as step (c) but placing your pointer at point. Label the intersection. (e) reate. is the angle bisector. a) b) Given the angle In part a measures 90 o, what is the measure of each bisected angle? c) d) isect E 11

12 e) f) Given the angle in part e measures 180 o, what is the measure of each bisected angle? Practice - NYTS (Now You Try Some) 1. isect each angle below. 2. a) On the diagram below, use a compass and straightedge to construct the bisector of. Label it Y. [Leave all construction marks.] b) What do you know about XY and ZY? Explain. *3. Which diagram shows the construction of a 45 angle? (1) (2) (3) (4) 12

13 Name: ate: ay 3&4LabLesson: isecting Segments and ngles & Geometry Terms Socrative Geometry (M1 L3) isecting Segments and ngles Socrative Geometry Terms 13

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18 Name: ate: ay 4: opy an ngle Geometry (M1 L3) Opening Exercises: 1. Using a compass and straightedge, construct a 60 o angle at R. 2. straightedge and compass were used to create the construction below. rc EF was drawn from point, and arcs with equal radii were drawn from E and F. Which statement is false? 1) 3) 2) 4) Term efinition Symbol/Notation ongruent Same and. (Geometry version of ) Line set of connected points extending in both directions. (annot be measured) Parallel Lines Lines that never. opying an ngle onstruction ' ' ' (a) Given an angle and a ray. ' (b) reate an arc of any size, such that it intersects both rays of the angle. Label those points and. ' ' (c) reate the same arc by placing your pointer at. The intersection with the ray is. ' ' ' (d) Place your compass at point and measure the distance from to. Use that distance to make an arc from. The intersection of the two arcs is. ' (e) raw the ray ' '. The angle has been copied. 18

19 Example 1: a) opy the angle shown below. ' b)what can you say about the measure of angle ( m ) and the measure of angle ( m ' )? Explain your answer. Example 2: Using a compass and straightedge, construct a copy of. Practice - NYTS (Now You Try Some) irections: opy the angles below. 1. Given. Make a copy of, ' ' '. ' E 19

20 2. Given EF. Make a copy of EF, ' E ' F '. F E' E Example 2: Given, can you think of a way to create a line parallel to through point? (Hint: How could copying an angle help you?) Practice - NYTS (Now You Try Some) 3. reate a parallel line to E through point F. E F 20

21 Name: ay 5: onstruct a Perpendicular isector ate: Geometry (M1L4) Opening Exercise: Using a compass and straightedge, construct the bisector of Term efinition iagram/notation Perpendicular Lines Two lines that intersect and form a angle at their point of intersection. isector (of a segment) line that cuts a segment in. Midpoint point that cuts a segment in. Perpendicular isector line that forms a angle at the point of intersection and cuts the segment in. Equidistant Equal Median ltitude segment connecting the vertex of a triangle to the of the opposite side. segment connecting the vertex of a triangle that is to the opposite side. 21

22 onstruct the perpendicular bisector of a line segment (a) Given (b) Place your pointer at, extend your compass so that the distance reaches. (c) Without changing your compass measurement, place your point at and create the same arc. The two arcs will intersect. Label those M (d) Place your straightedge on the paper and create. M (e) is the perpendicular bisector of Example 1: a) onstruct the perpendicular bisector of, label it YZ, and label the midpoint, M, of. b) What s true about the relationship between the lengths of Y and Y? c) What s true about the relationship between the lengths of Z and Z? d)what can be said in general about the relationship between points on a perpendicular bisector to the endpoints of the bisected segment? 22

23 Practice NYTS (Now You Try Some) 1.onstruct the perpendicular bisector of each segment below. 2. onstruct the perpendicular bisector of. 3. a) Find and label the midpoint of with the letter M. b) onnect M to vertex. What is vocabulary term for this segment? 23

24 onstruct a Perpendicular Line Through a Point Not on the Line Example 2: Using a compass and straightedge, construct a line that passes through point P and is perpendicular to line m. [Leave all construction marks.] Practice NYTO (Now You Try One!) Using a compass and straightedge, construct a line perpendicular to line marks.] through point P. [Leave all construction Example 3: a) Using a compass and straightedge, construct a perpendicular line from vertex to. [Leave all construction marks.] b) What is vocabulary term for this segment? 24

25 Name: ay 5and6 LabLesson: onstructions Practice ate: Geometry (M1) Opening Exercises: Using a compass and straightedge, construct the following: a)equilateral Triangle b) ngle isector c) opy an ngle d) Perpendicular isector e) Using a compass and straightedge, construct the line that is perpendicular to and that passes through point P. Show all construction marks. 25

26 Mixed Practice! Fill in the puzzle below using the vocabulary listed in the word bank. Word ank: ollinear ngle isector Obtuse Ray Isosceles Midpoint cute Segment Perpendicular Straight Radius onstruction ircle Equidistant Equilateral ROSS 3. n angle measuring more than 90 and less than 180 degrees 5. part of a line starting at one endpoint and going on forever through the other point on the line 6. Two noncollinear rays with a common endpoint form an 8. triangle with all sides and all angles congruent 10. point that divides a line segment into two congruent halves OWN 1. figure with a center point and all points the same distance away from the center 2. Point is said to be from and if = 4. part of a line between two endpoints 7. The distance from the center of the circle to any point on the circumference 9. ray that divides an angle into two congruent parts 11. triangle with two equal legs and two equal base angles 12. n angle less than 90 degrees 13. Points that lie on the same line 14. Lines that form a right angle 15. n angle measuring 180 degrees 16. set of instructions for drawing points, lines, circles and figures in a plane 26

27 Name: ay 6: onstructions and asic Notation Mixed Practice ate: Geometry (M1T) Part I: etermine whether the following are (T)rue or (F)alse. 1. n example of an acute angle would be an angle measuring 100 o. T or F 2. Perpendicular lines create 90 o angles at their point of intersection. T or F 3. correct name for the angle shown to the right could be MJH. T or F 4. ll angles in an equilateral triangle measure 90 o. T or F 5. In a geometric construction the ruler is used to take measurements T or F 6. Match the sides and angles described below with the correct notation in the below triangle diagram.. The side with a single hash mark.. The side with 2 hash marks.. The side with 3 hash marks.. The right angle marked with a small square. E. The angle marked with a single arc. F. The angle marked with 2 arcs. 1. JK 2. IK Notation 4. < IJK 5. < JKI 3. JI 6. < JIK 7. teacher finds a paper on the ground in the classroom. When she looks at it carefully she realizes it is from her geometry class because it has a construction on it. Which of the following constructions is NOT FOUN directly from this student s work? 1) The midpoint of 3) The perpendicular bisector of 2) perpendicular line to 4) The angle bisector of 27

28 8. ased on the construction below, which statement must be true? 1) 2) 3) 4) 9. What is the best description for the distance from Point to Point? E F 1) + 2EF 2) - EF 3) 2 - EF 4) 2 + EF 10. is shown below. Is it an equilateral triangle? Explain your response. 11. Given, construct a copy of it on the line below, label it XYZ. 28

29 12. Using a compass and a straightedge, construct the bisector of. [Leave all construction marks.] 13. reate a parallel line to through point by copying. 14. Using a compass and straightedge, construct a perpendicular line(altitude) from vertex to. [Leave all construction marks.] 29

30 15. onstruct the following. ) onstruct the perpendicular bisector of, label the perpendicular bisector XY. ) isect, label the bisector Z. 16. Using a compass and straightedge, construct an equilateral triangle with as a side. Using this triangle, construct a 30 angle with its vertex at. [Leave all construction marks.] 30