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Rule Of Congruency

The Congruency Of Two Triangles

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Rule Of Congruency

Question: In the adjoining figure, AB = AC and D is the mid-point of BC. Use SSS rule of congruency to show that-

i.  ABD congruent to  ACD
ii. AD is the bisector of angle A
iii. AD is perpendicular to BC

Solution:   

In the  ABD and ACD, 
Sides AB = AC
As D is the mid-point of the side BC
BD = DC
& AD = AD

According to SSS rule, which is applied for proving the congruency of two triangles. The SSS rule explains that, the congruency of the triangles depends on the feature of three equal sides in a triangle.

ABD is congruent to ACD

Therefore, angle BAD = angle CAD

Angle ADB = Angle ADC = 180°/2 = 90°

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