Question

In the adjoining figure, AB = AC and ZBAD = ZCAD. Show that
BD = CD
plz give me the answer of both​

Answer 1

Given,

AB = AC  

BD = DC

To prove,

ΔADB ≅ ΔADC

Proof,

In the right triangles ADB and ADC, we have:

Hypotenuse AB = Hypotenuse AC (given)

BD = DC (given)

AD = AD (common)

∴ ΔADB ≅ ΔADC

By SSS congruence property:

∠ADB = ∠ADC (corresponding parts of the congruent triangles) … (1)

∠ADB and ∠ADC are on the straight line.

∴∠ADB + ∠ADC =180o

∠ADB + ∠ADB = 180o

2 ∠ADB = 180o

∠ADB = 180/2

∠ADB = 90o

From (1): ∠ADB = ∠ADC = 90o

(ii) ∠BAD = ∠CAD (∵ corresponding parts of the congruent triangles)