Question

1. what are the methods to prove triangles are congruent?

Explanation:

There are several well - known methods in geometry to prove triangle congruence. Side - Side - Side (SSS) states that if the three sides of one triangle are equal to the three corresponding sides of another triangle, the triangles are congruent. Side - Angle - Side (SAS) means if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, the triangles are congruent. Angle - Side - Angle (ASA) is when two angles and the included side of one triangle are equal to two angles and the included side of another triangle, the triangles are congruent. Angle - Angle - Side (AAS) occurs when two angles and a non - included side of one triangle are equal to the corresponding two angles and non - included side of another triangle, the triangles are congruent. Hypotenuse - Leg (HL) is used for right - angled triangles, where if the hypotenuse and one leg of a right - angled triangle are equal to the hypotenuse and one leg of another right - angled triangle, the two right - angled triangles are congruent.

Answer:

Side - Side - Side (SSS), Side - Angle - Side (SAS), Angle - Side - Angle (ASA), Angle - Angle - Side (AAS), Hypotenuse - Leg (HL) for right - angled triangles.