The SSS rule states that:- If three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent. In the diagrams below, if AB = RP, BC = PQ and CA = QR, then triangle ABC is congruent to triangle RPQ. Side - Side - Side (SSS) Rule Side-Angle-Side (SAS) Rule Side-Angle-Side is a rule used to prove whether a given set of triangles are congruent. The SAS rule states that :- If two sides and the included angle of one triangle are equal to two sides and included angle of another triangle, then the triangles are congruent. An included angle is an angle formed by two given sides. Included and Non-included angle:- Included Angle Non-included angle For the two triangles below, if AC = PQ, BC = PR and angle C = angle P , then using the SAS rule, triangle ABC is congruent to triangle QRP congruent triangles Angle-Side-Angle (ASA) Rule Angle-side-angle is a rule used to prove whether a given set of triangles are congruent. The ASA rule states that If two angles and the included side of one triangle are equal to two angles and included side of another triangle, then the triangles are congruent. Angle-Angle-Side (AAS) Rule Angle-angle-side is a rule used to prove whether a given set of triangles are congruent. The AAS rule states that If two angles and a non-included side of one triangle are equal to two angles and a non-included side of another triangle, then the triangles are congruent. In the diagrams below, if AC = QP, angle A = angle Q, and angle B = angle R, then triangle ABC is congruent to triangle QRP. read less

There are the following steps to prove that two triangles are similar:- 1. AAA Test (angle angle angle): All three pairs of corresponding angles are the same. 2. SSS Test (side side side): All three pairs of corresponding sides are in the same proportion. 3. SAS Test (side angle side): Two pairs of sides are in the same proportion and the angle between them is equal.

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