Congruence of Triangles

The equality of triangles is called the congruence of triangles.

Introduction

There are some types of triangles in geometry. In some cases, the triangles may have same properties, which make them equal geometrically. The word “equal” is expressed by another word “congruence” in mathematics.

The triangles are called congruent triangles when their corresponding angles are equal and also the lengths of their corresponding sides are equal.

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Criterion

There are five possible criteria in geometry for the congruence of triangles.

When the lengths of three sides of a triangle are equal to the lengths of corresponding sides of other triangle.
When the lengths of two sides and the included angle of a triangle are equal to the lengths of corresponding sides and the included angle of other triangle.
When two angles and the included side of a triangle are equal to the corresponding angles and the length of included side of other triangle.
When two angles and one side of a triangle are equal to the corresponding angles and the length of one side of other triangle.
When the lengths of hypotenuse and one side of a right triangle are equal to the lengths of hypotenuse and corresponding side of other right angled triangle.

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