Congruence of Triangles

Proving if some shapes, especially triangles, are congruent is an important part of the study of geometry. This lecture series discusses the three theorems that establish the congruence of triangles.

Practice

Prove triangle congruence - Answers

1. Holden used a criterion that does not guarantee congruence.

	Statement	Reason
1	$\overline{Q R} \cong \overline{T R}$	Given
2	$\overline{P R} \cong \overline{S R}$	Given
3	$\angle Q R P \cong \angle T R S$	Vertical angles are congruent.
4	$\triangle P Q R \cong \triangle S T R$	Side-angle-side congruence

	Statement	Reason
1	$m \angle B A C=m \angle D A C=51^{\circ}$	Given.
2	$A B=A D=4$	Given
3	$A C=A C$	Segments are the same length as themselves.
4	$\triangle A B C \cong \triangle A D C$	Side-angle-side congruence

4. Jordy used a criterion that does not guarantee congruence.