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://staging-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=AKIAXQCCIHWF37H2AMFB%2F20240703%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240703T083125Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=89ca1fc71b0d8c791229cb9fcafd425f82a6929f0bd6a19d0137cf79b5ecb072)
Solution
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Problem 2
These two figures are congruent, with corresponding points marked.
![Transformation quadrilaterals.](https://staging-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=AKIAXQCCIHWF37H2AMFB%2F20240703%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240703T083125Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=a7c980c53b79d5cf516a57ea6e169652095b093fe6550f9187fbc0d2aa0a661f)
- 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://staging-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=AKIAXQCCIHWF37H2AMFB%2F20240703%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240703T083125Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=d56ece2125e21b2fcbc6c0372ba487d155904ff8ab663c9c16e237c72ff64c39)
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://staging-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=AKIAXQCCIHWF37H2AMFB%2F20240703%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240703T083125Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=375416ebff3359593ab0804e7caab51f5e2704df2def47d14a3eb04ab639ddb8)
Show, using measurement, that these two figures are not congruent.
Solution
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