Math, asked by MDNadeem6803, 11 months ago

Abc is an isosceles triangle in which ab=ac. Side ba is produced to d such that ad =ab show that angle bcd is aright angle

Answers

Answered by HeAvEnPrlnCesS
1

Given: ∆ABC is an isosceles ∆.

AB = AC and AD = AB

To Prove:

∠BCD is a right angle.

Proof:

In ΔABC,

AB = AC (Given)

⇒ ∠ACB = ∠ABC (Angles opposite to the equal sides are equal.)

In ΔACD,

AD = AB

⇒ ∠ADC = ∠ACD (Angles opposite to the equal sides are equal.)

Now,

In ΔABC,

∠CAB + ∠ACB + ∠ABC = 180°

⇒ ∠CAB + 2∠ACB = 180°

⇒ ∠CAB = 180° – 2∠ACB — (i)

Similarly in ΔADC,

∠CAD = 180° – 2∠ACD — (ii)

also,

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

Adding (i) and (ii)

∠CAB + ∠CAD = 180° – 2∠ACB + 180° – 2∠ACD

⇒ 180° = 360° – 2∠ACB – 2∠ACD

⇒ 2∠ACB + 2∠ACD= 360-180

⇒ 2(∠ACB + ∠ACD) = 180°

⇒ ∠BCD = 90°

=========================================

Answered by TheUnicornGirl
3

your answer is in attachment....

Attachments:
Similar questions