FTCE General Knowledge Math Practice Test

When are two triangles considered congruent?

1. When they have the same area

2. When their corresponding sides and angles are congruent

3. When they have one angle in common

4. When they are of the same shape

The correct answer is: When their corresponding sides and angles are congruent

Two triangles are considered congruent when their corresponding sides and angles are congruent. This means that if you can show that each side of one triangle is equal in length to a corresponding side of another triangle, and each angle of one triangle is equal to the corresponding angle of the other triangle, then the two triangles are congruent. This establishes that the triangles are identical in both shape and size, allowing them to be perfectly superimposed onto one another. Congruence goes beyond merely having the same area or having one angle in common, as these criteria do not guarantee that all corresponding sides and angles match. While having the same shape might suggest that the triangles are similar, it does not account for size, which is why congruence requires a more strict comparison of corresponding components. Thus, congruency relies on the comprehensive comparison of both sides and angles.