Mastering Congruent Triangles: The Methods To Prove Congruence

congruent triangles

2 triangles are congruent if and only if all pairs of corresponding sides and angles are congruent

Congruent triangles are two triangles that have the same shape and size. In other words, all pairs of corresponding angles and sides are equal in both triangles. Congruent triangles are denoted by the symbol ≅.

To prove that two triangles are congruent, one of the following methods can be used:

1. Side-Side-Side (SSS) Criterion: If three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent.

2. Side-Angle-Side (SAS) Criterion: If two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the triangles are congruent.

3. Angle-Side-Angle (ASA) Criterion: If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the triangles are congruent.

4. Right-Angle-Hypotenuse-Side (RAHS) Criterion: If the hypotenuse and a side of one right triangle are equal to the hypotenuse and a side of another right triangle, then the triangles are congruent.

5. Hypotenuse-Leg (HL) Criterion: If the hypotenuse and a leg of one right triangle are equal to the hypotenuse and a leg of another right triangle, then the triangles are congruent.

It is important to remember that congruence is a relation between pairs of objects, in this case, two triangles. Congruence does not depend on the size of the triangles, but only on the shape and relative positions of their parts.

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