Lesson 13
Congruence
Problem 1
Which of these four figures are congruent to the top figure?
![Five quadrilateral figures each with 3 blue dots.](https://cms-im.s3.amazonaws.com/XzFN7mdLxa8MuH5ZosNMDRge?response-content-disposition=inline%3B%20filename%3D%228.1.C.PP.Image.13.2.png%22%3B%20filename%2A%3DUTF-8%27%278.1.C.PP.Image.13.2.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T000225Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=ba289506b97c12af63c06feed769084784d2403e0b8456b1a94b639dc3cffd18)
A
B
C
D
Solution
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Problem 2
These two figures are congruent, with corresponding points marked.
![Transformation quadrilaterals.](https://cms-im.s3.amazonaws.com/7vAzH8QH5vB334hLeJkF6Ywp?response-content-disposition=inline%3B%20filename%3D%228-8.1.C.PP.Image.10.2.png%22%3B%20filename%2A%3DUTF-8%27%278-8.1.C.PP.Image.10.2.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T000225Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=5855c0386fdcebd8f285214aec10fe992ff14a7b47889f75bb76c2eec3043a30)
- Are angles \(ABC\) and \(A'B'C'\) congruent? Explain your reasoning.
- Measure angles \(ABC\) and \(A’B’C’\) to check your answer.
Solution
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Problem 3
Here are two figures.
![Two figures, A and B. Figure A is an oval, wider than is tall. Figure B appears circular.](https://cms-im.s3.amazonaws.com/b186PDVNrXuvFdEvJeDVxQ3y?response-content-disposition=inline%3B%20filename%3D%228-8.1.C.13.PP.Image.01.png%22%3B%20filename%2A%3DUTF-8%27%278-8.1.C.13.PP.Image.01.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T000225Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=82c8b3034cebc676a46e7f316823823f598350b0f833d65098d72d860a386636)
Show, using measurement, that these two figures are not congruent.
Solution
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Problem 4
Each picture shows two polygons, one labeled Polygon A and one labeled Polygon B. Describe how to move Polygon A into the position of Polygon B using a transformation.
Solution
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(From Unit 1, Lesson 3.)