Question

AABC is an isosceles triangle in which AB=AC. Side BA is produced to D such that AD = AB (see Fig. 7.34). Show that BCD is a right angle.​

Answer 1

Answer:

Solution

verified

Verified by Toppr

In △ABC, we have

AB=AC ∣ given

∠ACB=∠ABC ... (1) ∣ Since angles opp. to equal sides are equal

Now, AB=AD ∣ Given

∴AD=AC ∣ Since AB=AC

Thus , in △ADC, we have

AD=AC

⇒∠ACD=∠ADC ... (2) ∣ Since angles opp. to equal sides are equal

Adding (1) and (2) , we get

∠ACB+∠ACD=∠ABC+∠ADC

⇒∠BCD=∠ABC+∠BDC ∣ Since∠ADC=∠BDC

⇒∠BCD+∠BCD=∠ABC+∠BDC+∠BCD ∣ Adding ∠BCD on both sides

⇒2∠BCD=180

∣ Angle sum property

⇒∠BCD=90

Hence, ∠BCD is a right angle.

Step-by-step explanation:

step by step

helpful answer