Quant Basics: Isosceles Triangle Congruence Theorem

Among the many types of triangles, a unique case is of the isosceles triangle. An isosceles triangle is a triangle where two of its sides are equal (or congruent). Obviously, this special triangle is governed by special qualities represented by the isosceles triangle theorem.

Now, let us consider an isosceles triangle ABC (in the figure above).

In the above example, the side AB is equal to side AC

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The theorem states that if two sides of a triangle are congruent, the angles opposite them are also equal or congruent. In the above example, angle B is congruent to angle C.

Obviously, the converse of the theorem i.e when two angles of a triangle are congruent the sides of the angle are congruent is also true. You can use this information to determine whether a triangle is congruent or not.

Congruent Isosceles Triangle

 

Another interesting thing about an isosceles triangle is that if you draw an altitude (AG), it bisects the base and vertex angle.

In the above example,

The side BG is congruent to side GC

Angle BAG is congruent to angle CAG.

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