Question

If the bisector of the vertical angle bisects the base of the triangle. Prove that the triangle is isosceles triangle.

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Answer 1

Step-by-step explanation:

Construction

Produce AD to E such that AD=DE Join EC

Proof : In △ADB and △EDC  

BD=CD ( given)

AD=ED ( by construction)

∠ADB=∠EDC ( vertically opposite angles)

∴△ADB≅△EDC ( SAS congruence)

∴AB=ED−−−−−(1) ( by CPCT)

and ∠BAD=∠CED ( by CPCT)

But ∠BAD=∠CAD (given)

∴∠CAD=∠CED

∴AC=CE−−−−−−−(2) ( sides opposite to equal angles of a triangle are equal.

From (1) and (2),  AB=AC

∴△ABC is isosceles.

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Answer 2

Answer:

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