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://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=20240727T005951Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=3816a0260b27a1164afdc198dc4d7b9580b9800868c99efba658a18bf3a8e3fa)
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=20240727T005951Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=0e1f6ca1ca56d6cdc4ebda47bd464a591e5d6f19db610b5a072bd62c597faaf5)
- 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://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=20240727T005951Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=eaa3883e382653909dc9d6c5e17decc62da06cec0195aa7a9131abff8805eed6)
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://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=20240727T005951Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=c8423f466b1ffa7ba50d6026cd64a07404d2662e905ce435a86207666e2d76a6)
Show, using measurement, that these two figures are not congruent.