Question

Prove that:

1. ∆ ABD ≅ ∆ ACD
2. ∠B = ∠C
3. ∠ADB = ∠ADC
4. ∠ADB = 90°

Answer 1

Given: In the figure,
AB = AC 
BD = CD

To prove:

1. Δ ABD ≅ Δ ACD
2. ∠B = ∠C
3. ∠ADB = ∠ADC
4. ∠ADB = 90°

Proof: In Δ ABD and Δ ACD
AD = AD   ...(common)
AB = AC   ...(given)
BD = CD   ...(given)

(i) ∴ Δ ABD ≅ Δ ACD   ...(SSS axiom)

(ii) ∴ ∠B = ∠C   ...(c.p.c.t.)

(iii) ∠ADB = ∠ADC   ...(c.p.c.t.)

But ∠ADB + ∠ADC = 180°   ...(Linear pair)

∴ ∠ADB = ∠ADC

(iv) ∠ADB = ∠ADC

= `(180°)/2`

= 90°