Q24 of 97 Page 187

Prove that median from the vertex of an isosceles triangle is the bisector of the vertical angle.

Given: ∆ABC is isosceles triangle where AB = AC and BD = DC


To prove: ∠BAD = ∠DAC


Proof:



In ∆ABD and ∆ADC


AB = AC …given


BD = DC …given


AD = AD … common side


Thus by SSS property of congruence,


∆ABD ≅ ∆ADC


Hence, we know that, corresponding parts of the congruent triangles are equal


∠BAD = ∠DAC


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