## 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 exactly the same shape and size. In other words, the corresponding sides and angles of the triangles are equal.

When we say two triangles are congruent, we can use the symbol ≅ to represent that they are the same size and shape. To prove that two triangles are congruent, we must show that all three pairs of corresponding sides and angles are equal.

There are several methods we can use to prove that two triangles are congruent, such as the Side-Side-Side (SSS), Side-Angle-Side (SAS), Angle-Side-Angle (ASA), Angle-Angle-Side (AAS) and Hypotenuse-Leg (HL) methods.

SSS: If the three sides of one triangle are equal to the three sides of another triangle, then the triangles are congruent.

SAS: If any two sides and the included angle of one triangle are equal to any two sides and the included angle of another triangle, then the triangles are congruent.

ASA: If any two angles and the included side of one triangle are equal to any two angles and the included side of another triangle, then the triangles are congruent.

AAS: If any two angles and a non-included side of one triangle are equal to any two angles and the corresponding non-included side of another triangle, then the triangles are congruent.

HL: 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.

Congruent triangles have many properties that we can use to solve problems in geometry. For example, if two triangles are congruent, we know that their corresponding sides and angles are equal, and we can use this fact to solve for unknown measurements or angles.

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