# Triangles

## A triangle is a closed plane figure made up of three line segments. Two figures are congruent, if they have same shape and size. Two triangles are congruent if all the sides and all the angles of one triangle are equal to the corresponding sides and angles of the other triangle. SAS Congruence rule: Two triangles are congruent if two sides and the included angle of one triangle are equal to the two sides and the included angle of the other triangle. ASA Congruence rule: Two triangles are congruent if two angles and the included side of one triangle are equal to two angles and the included side of other triangle. AAS Congruence rule: Two triangles are congruent, if any two pairs of angles and one pair of the corresponding sides are equal. RHS Congruence rule: Two right triangles are congruent, if the hypotenuse and one side of a triangle are respectively equal to the hypotenuse and one side of the other triangle. SSS Congruence rule: If three sides of one triangle are equal to three sides of the other triangle, then the two triangles are congruent. A triangle in which two sides are equal is called an isosceles triangle. Angles opposite to equal side of an isosceles triangle are equal. The sides opposite to equal angles of a triangle are equal. If two sides of a triangle are unequal, the angle opposite to the longer side is larger (or greater). In any triangle, the side opposite to the larger (greater) angle is longer. The sum of length of any two sides of a triangle is greater than the third side. The difference of any two sides of a triangle is less than the third side.

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