Question

ABC and DBC are two isosceles triangle on the same base BC. Show that ABD=ACD

Answer 1

Step-by-step explanation:

Given

ΔABC is an isosceles triangle

So, AB=AC ------> equation 1

ΔDBC is an isosceles triangle

So, DB=DC ------> equation 2

To prove

ABD=ACD

Proof

Let us join AD

We take ΔABD and ΔACD

In ΔABD and ΔACD

AB=AC (From equation 1)

BD=CD (From equation2)

AD=AD (common)

Therefore, ΔABD congruent to ΔACD (SSS congruence rule)

angle ABD = angle ACD (cpct)

Hence Proved

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