Slide, Flip, Turn: The Latest Dance Craze?
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1 Lesson.1 Assignment Name Date Slide, Flip, Turn: The Latest Dance Craze? Translating, Rotating, and Reflecting Geometric Figures 1. Transform rectangle JKLM so it sits in the shaded rectangle in Quadrant III. y M J L K x a. How many different transformations will it take to place rectangle JKLM in the shaded area in Quadrant III? b. Describe and perform a transformation to move rectangle JKLM to Quadrant II. Identify the coordinates of the vertices of the transformed rectangle, J9K9L9M9. Explain how you determined your answer. Chapter Assignments 139
2 Lesson.1 Assignment page 2 c. Describe and perform the transformation that can be used to move rectangle J9K9L9M9 to Quadrant III. Identify the coordinates of the vertices of the transformed rectangle, J0K0L0M0. Explain how you determined your answer. d. Could a different transformation(s) be used to move rectangle JKLM to Quadrant III? Explain your reasoning. 2. Consider figure QRST. y T S x Q R Ramona states that there are three ways to transform QRST to place its image in the shaded area in Quadrant II. Translate QRST vertically 13 units up, then horizontally 15 units to the left. Reflect QRST over the x-axis then over the y-axis. Rotate QRST 180 counterclockwise (or clockwise) about the origin. 140 Chapter Assignments
3 Lesson.1 Assignment page 3 Name Date a. Without graphing, determine the coordinates of the vertices of the image for each of the transformations Ramona listed. Explain how you determined your answers. b. Which transformation would you recommend that Ramona choose? Explain your reasoning. c. Perform the transformation you chose in part (b). Chapter Assignments 141
4 142 Chapter Assignments
5 Lesson.2 Assignment Name Date All the Same to You Congruent Triangles 1. Analyze triangle ABC. y B x 28 A C a. Describe a transformation that can be performed on n ABC that will result in a triangle being created in Quadrant I. b. Will the transformation you described preserve the size and shape of the triangle? Explain your reasoning. c. Perform the transformation and name the new triangle DEF. d. List the coordinates for the vertices of both triangles. e. Using the names of the vertices, write a triangle congruence statement for the triangles. Chapter Assignments 143
6 Lesson.2 Assignment page 2 f. Using your congruence statement, identify the congruent angles. g. Using your congruence statement, identify the congruent sides. 2. Analyze triangle MNO. y N x M O a. Describe a transformation that can be performed on n MNO that will result in a triangle being created in Quadrant III. b. Will the transformation you described preserve the size and shape of the triangle? c. Perform the transformation and name the new triangle PQR. 144 Chapter Assignments
7 Lesson.2 Assignment page 3 Name Date d. List the coordinates for the vertices of both triangles. e. Using the names of the vertices, write a triangle congruence statement for the triangles. f. Using your congruence statement, identify the congruent angles. g. Using your congruence statement, identify the congruent sides. Chapter Assignments 145
8 146 Chapter Assignments
9 Lesson.3 Assignment Name Date Side-Side-Side Side-Side-Side Congruence Theorem 1. Analyze the triangles shown. K 8 y 6 L 4 J S x R 28 T a. Are the two triangles shown on the grid congruent? Show and explain how you determined your answer. Chapter Assignments 14
10 Lesson.3 Assignment page 2 b. Juan says the triangle congruency statement for these triangles should be njkl > nrst. Natsu says the triangle congruency statement for these triangles should be njkl > nsrt. Who is correct? Explain your reasoning. 148 Chapter Assignments
11 Lesson.4 Assignment Name Date Side-Angle-Side Side-Angle-Side Congruence Theorem 1. Analyze the triangles shown. y O N K 22 M x J 28 L a. Use the distance formula and a protractor to prove that the two triangles shown on the grid are congruent by SAS. Show your work. Chapter Assignments 149
12 Lesson.4 Assignment page 2 b. Mark the triangles to show which sides and angles are congruent. c. Write a congruency statement for the triangles. 150 Chapter Assignments
13 Lesson.5 Assignment Name Date You Shouldn t Make Assumptions Angle-Side-Angle Congruence Theorem 1. Emerson wants to translate n ABC and then reflect it over the y-axis to form a new triangle in Quadrant II. She uses what she knows about transformations to determine the vertices of n A9B9C9 before performing the transformations. B9 8 y 6 C9 4 2 A B 6 8 x C 28 A a. Briefly describe how Emerson can use the ASA Congruence Theorem to determine whether or not she transformed n ABC, such that the image is congruent to the pre-image. b. Connect points A9, B9, and C9. Use a protractor to determine the measure of two corresponding angles in each triangle. Chapter Assignments 151
14 Lesson.5 Assignment page 2 c. Calculate the length of the included side of n ABC and n A9B9C9. Show your work. d. Did Emerson perform the transformations on n ABC so that the image is congruent to the pre-image? Explain your reasoning. 152 Chapter Assignments
15 Lesson.6 Assignment Name Date Ahhhhh... We re Sorry We Didn t Include You! Angle-Angle-Side Congruence Theorem 1. Describe and use AAS to prove that triangle LMN is congruent to triangle QRS. M 8 y 6 4 L 2 N R 6 8 x Q S Chapter Assignments 153
16 Lesson.6 Assignment page 2 2. Triangles ABC and DFG are given. A D 39 B C F 90 G a. Side BC of n ABC is congruent to side FG of ndfg. Mark the triangles to show that these sides are congruent. b. Do you have enough information to determine whether n ABD is congruent to ndfg? Explain your reasoning. c. Without using a protractor, calculate the measure of /BAC. Show your work. Write the measure on the triangle. d. Now, do you have enough information to determine that n ABC is congruent to ndfg? Write congruence statements to justify your reasoning. 154 Chapter Assignments
17 Lesson. Assignment Name Date Congruent Triangles in Action Using Congruent Triangles 1. Use triangle congruency proofs to prove the statement using the given information. a. A B Given: /A > /E AB > EC Prove: CB > DC C D E b. A Given: FE > BC AF i CD, AB i ED B C F E Prove: nabf > ndec D Chapter Assignments 155
18 Lesson. Assignment page 2 c. A E Given: nabc is equilateral AC i ED AB > ED B C D Prove: /E > /ACD d. A Given: AD is a perpendicular bisector of BC AB > AC Prove: nabd > nacd B D C 156 Chapter Assignments
19 Lesson. Assignment page 3 Name Date e. E B F Given: EF i AD BC is angle bisector of /ABD BC is the perpendicular bisector of EF Prove: ncab > ncdb A C D Chapter Assignments 15
20 Lesson. Assignment page 4 2. Write the information needed in each situation to prove that the triangles are congruent, and state the postulate, or state that there is already enough information to prove the specified triangles congruent, and state the postulate. a. B Given: /B > /D Prove: nabc > nadc A C D b. E C B A D Given:/BAC > /DAE AE > AC A is the midpoint of BD Prove: nbea > ndca c. B Given: /A and /D are right angles A P D C Prove: nbap > ncdp 158 Chapter Assignments
Slide, Flip, Turn: The Latest Dance Craze?
Lesson.1 Assignment Name Date Slide, Flip, Turn: The Latest Dance Craze? Translating, Rotating, and Reflecting Geometric Figures 1. Transform rectangle JKLM so it sits in the shaded rectangle in Quadrant
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