Congruence and Congruence Transformations Examples

Name the congruent triangles in the figure.

First, we need to identify which triangles we're talking about, here. We can match up the congruent angles. For instance, since ∠A ≅ ∠D, they should have the same placement in the names of both triangles. Both angles with vertex B are right angles, so we can say that ∆ABC ≅ ∆DBC.

Compared to ∆ABC, which moves have not yet been performed on ∆DBC? 

The two triangles look like mirror images of each other. That means ∆DBC has already been flipped, or reflected, from ∆ABC. The remaining moves that have not yet been used are sliding, or translating, the triangle and turning, or rotating, it either clockwise or counterclockwise.

Two triangles with corresponding congruent angles are always congruent. Is this statement true or false?

One of the best ways to prove whether a statement is true or false is to assume it as true until we come up with a counterexample. Let's try assuming it's true. That statement translates to saying that if a triangle's corresponding angles are the same measures, its corresponding angles and its corresponding sides must be equal in measure.

If that's true, all equilateral triangles must be congruent (because every angle in an equilateral triangle is 60°). Another way of saying that is: All equilateral triangles must have the same size. Is that true? Of course not!

An equilateral triangle could have sides of 6 inches or 6 miles, and its angles would still be 60°. That means the statement is false.