Congruency of Triangles

Two triangles are said to be congruent if they are exactly alike in all respects. If one triangle is placed on the other, the two triangles will coincide exactly with each other, i.e., the vertices of the first triangle will coincide with those of the second. In a pair of congruent triangles, the sides opposite to equal angles are known as corresponding sides and the angles opposite to equal sides are known as corresponding angles.

Here, in ∆KLM and ∆XYZ, ∠K = ∠X, ∠L = ∠Y and ∠M = ∠Z.

Also, KL = XY, LM = YZ and KM = XZ.

As the two triangles are exactly equal in all respects, they are congruent.

Symbolically, we write ∆KLM ≅ ∆XYZ.

Congruent triangles are equal in area.

9th Grade Math

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