Question

Congruent Polygons:Find congruent figures and write a congruence statement. Prove that they are congruent by finding a rigid motion that maps one onto the other.

Answer 1

Given in figure 5 : 3 right angle triangles

For the triangle ABC :

The angle A is the right angle

AB = 5

AC = 2

For the triangle DEF:

The angle E is the right angle

EF = 4

DE = 2

For the triangle XYZ

The angle Y is the right angle

XY = 5

YZ = 2

So, by comparing the data of the triangles:

The triangle ABC is congruent to the triangle YXZ

By SAS [ side - angle - side ]

The rigid motion that can map one to the other will be:

By rotating the triangle YXZ , 90 degree clockwise a round the point Z, then make a translation 6 units to the right , We will get the triangle ABC