Lesson 11
Congruence
Let’s decide if two figures are congruent.
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%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T151053Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=354b335e94e1bb34f0a9dc8313a85ec61eaace83aa8a38e91fa31acd63813c07)
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%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T151053Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=b886e37093eda2604797a3a4a3569a7b48d74d147a369f4a10e79f53e2031bbf)
- Are angles \(ABC\) and \(A'B'C'\) congruent? Explain your reasoning.
- Measure angles \(ABC\) and \(A’B’C’\) to check your answer.
Problem 3
For each pair of shapes, decide whether or not the two shapes are congruent. Explain your reasoning.
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%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T151053Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=c7f76523971c7acaf29985de299a0027e71231d9e2d4c0c709bc1a28cdce562c)
A:
A
B:
B
C:
C
D:
D
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%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T151053Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=1d7a3a32673d7f1cb698d7af369e68efb857a9876e58ebd052872e822de9a1a4)
Show, using measurement, that these two figures are not congruent.