Congruent Triangle Proofs Worksheets

How to Prove Triangles are Congruent - When two triangles are congruent, one triangle can be moved through more rigid motions to coincide with another triangle. All the corresponding angles and sides will be congruent. When triangles are congruent, six facts are always true: Corresponding sides are congruent. Corresponding angles are congruent. The best part is when you are trying to prove the congruency of a triangle. It is not necessary to prove all the six points to show their congruency. Below are some of the methods of proving congruency. Here is how you prove congruent triangles by following the ordered combinations. SSS (Side-Side-Side) - If the three sides of a triangle are congruent to another triangle, then the two triangles are congruent. SSS (Side-Angle-Side) - If two sides and included angle of one of the triangles are congruent to corresponding parts of another triangle, these triangles are congruent. ASA (Angle-Side-Angle) - If two angles and included side of one of the triangles are congruent to the corresponding parts of another triangle, the two triangles are congruent. AAS (Angle-Angle-Side) - If two angles and a non-included side of one triangle are congruent to the corresponding sides of another triangle, the triangles are congruent to each other. HL (Hypotenuse-Leg) - If the hypotenuse and leg of one triangle are congruent to the corresponding part of another right-angled triangle, the triangle is congruent.