# how to understand congruence of triangles . please tell me today because i have to prepare for test

## Congruent Triangles

Triangles that have exactly the same size and shape are called congruent triangles. The symbol for congruent is ≅. Two triangles are congruent when the three sides and the three angles of one triangle have the same measurements as three sides and three angles of another triangle. The triangles in Figure 1 are congruent triangles. Figure 1 Congruent triangles.

## Corresponding parts

Example 1: If Δ PQR ≅ Δ STU which parts must have equal measurements? These parts are equal because corresponding parts of congruent triangles are congruent.

## Tests for congruence

To show that two triangles are congruent, it is not necessary to show that all six pairs of corresponding parts are equal. The following postulates and theorems are the most common methods for proving that triangles are congruent (or equal). Figure 2 The corresponding sides (SSS) of the two triangles are all congruent. Figure 3 Two sides and the included angle (SAS) of one triangle are congruent to the corresponding parts of the other triangle. Figure 4 Two angles and their common side (ASA) in one triangle are congruent to the corresponding parts of the other triangle. Figure 5 Two angles and the side opposite one of these angles (AAS) in one triangle are congruent to the corresponding parts of the other triangle. Figure 6 The hypotenuse and one leg (HL) of the first right triangle are congruent to the corresponding parts of the second right triangle. Figure 7 The hypotenuse and an acute angle (HA) of the first right triangle are congruent to the corresponding parts of the second right triangle. Figure 8 The legs (LL) of the first right triangle are congruent to the corresponding parts of the second right triangle. Figure 9 One leg and an acute angle (LA) of the first right triangle are congruent to the corresponding parts of the second right triangle.

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