Lesson 11
Congruence
Problem 1
- Show that the two pentagons are congruent.
- Find the side lengths of \(ABCDE\) and the angle measures of \(FGHIJ\).
![Two figures A B C D E and F G H I J on a square grid.](https://cms-im.s3.amazonaws.com/gKjfo5chm6aJ83jsKkR5nrEG?response-content-disposition=inline%3B%20filename%3D%228-8.1.C.PP.Image.07.png%22%3B%20filename%2A%3DUTF-8%27%278-8.1.C.PP.Image.07.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=20240727T001643Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=a6c769dc852c46ca79abd1430cbe36d2005fc42bdcbbe63e4f518af674aea76c)
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=20240727T001643Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=2a1d069db338bc3830c34b62f318be15685a8b688893650bf9dfadecca88122f)
- 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
For each pair of shapes, decide whether or not the two shapes are congruent. Explain your reasoning.
Solution
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Problem 4
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=20240727T001643Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=759db328770d07653e052bdd6e8f67cb945aa2880cd094ec8c87b8d77fa9f1ab)
A
B
C
D
Solution
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Problem 5
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=20240727T001643Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=2f606bace768cac6786cb6a55b8259a6a548430f7a5ed597a6b38ecb6c9efe74)
Show, using measurement, that these two figures are not congruent.
Solution
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