Lesson 13

Congruence

Let’s find ways to test congruence of interesting figures.

Problem 1

Which of these four figures are congruent to the top figure?

Five quadrilateral figures each with 3 blue dots.
A:

A

B:

B

C:

C

D:

D

Problem 2

These two figures are congruent, with corresponding points marked.

Transformation quadrilaterals.
  1. Are angles \(ABC\) and \(A'B'C'\) congruent? Explain your reasoning.
  2. Measure angles \(ABC\) and \(A’B’C’\) to check your answer.

Problem 3

Here are two figures.

Two figures, A and B. Figure A is an oval, wider than is tall. Figure B appears circular.

Show, using measurement, that these two figures are not congruent.

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.

  1.  
    Two quadrilaterals, polygon A and polygon B on a grid. Every point of polygon B is a reflection of polygon A.
  2.  
    Two triangles, polygon A and polygon B on a grid. Every point of polygon B is a rotation of polygon A.
  3.  
    Two figures A and B on a grid. Every point of figure B is 1 unit up and 3 units to the right of figure A.
(From Unit 1, Lesson 3.)