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Question: Using congruency of triangles prove that bisector of the vertex angle of an isosceles triangle is perpendicular to the base.



Steps to derive

1 Figure:


2 AB‾ ≅ AC‾

3 Let AD‾ be the bisector of ∠A
 [Reflective property.]

4 Hence, ∠ABD ≅ ∠ACD

5 AB‾ ≅ AC‾

6 ΔADB ≅ ΔADC
 [By SAS postulate.]

7 Hence, ∠BDA ≅ ∠CDA
 [From step 6.]

8 So, BD‾ ⊥ AD‾



Hence the right answer is Option

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