Question

please give me the answer ​

Answer 1

Answer:

Given:-ABC is an isosceles triangle

→AB=AC

also,AD=AB

To prove:- Angle BCD is a right angle

Proof:- Let us Consider ΔABC,

AB = AC (Given)

Also, ACB = ABC (angles opposite to the equal sides are equal)

Now, Let us consider ΔACD,

AD = AB (Given)

Also, ADC = ACD (angles opposite to the equal sides are equal)

Now,

In ΔABC,

CAB + ACB + ABC = 180°

So, CAB + 2ACB = 180°

⇒ CAB = 180° – 2ACB — (i)

Similarly, in ΔADC,

CAD = 180° – 2ACD — (ii)

also,

CAB + CAD = 180° (BD is a straight line.)

Adding (i) and (ii) we get,

CAB + CAD = 180° – 2ACB + 180° – 2ACD

⇒ 180° = 360° – 2ACB-2ACD

⇒ 2(ACB+ACD) = 180°

⇒ BCD = 90°

Hence Proved