Question

If the bisector of vertical angle of a triangle bisects the base, prove that the triangle is an isosceles triangle

Answer 1

Given:
In ∆ABC ,
AD bisects ∠BAC, & BD= CD

To Prove:
AB=AC

Construction:
Produce AD to E such that AD=DE & then join E to C.

Proof:

In ∆ADB & ∆EDC
AD= ED ( by construction)
∠ADB= ∠EDC. (vertically opposite angles (

BD= CD (given)

∆ADB congruent ∆EDC (by SAS)

Hence, ∠BAD=∠CED......(1) (CPCT)

∠BAD=∠CAD......(2). (given)

From eq.1 &2
∠CED =∠CAD......(3)

AB=CE (CPCT).......(4)

From eq 3 as proved that

∠CED=∠CAD

So we can say CA=CE......(5)

[SIDES OPPOSITE TO EQUAL ANGLES ARE EQUAL]

Hence, from eq 4 & 5

AB = AC

HENCE THE ∆ IS ISOSCELES..

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Hope this will help you....

Answer 2

Answer:

here is your answer......