Question

In the figure, AD bisects ∠A and AD ⊥ BC. Show that △ADB ≅ △ADC.​

Answer 1

Given:

∠A = ∠C ( AD bisects ∠A )

AD ⊥ BC

∠ADC = 90°

To Prove:

△ADB ≅ △ADC

Proof:

In △ADB and △ADC,

∠BAD = ∠CAD ( AD bisects ∠A )

AD = AD ( Common )

∠ADB = ∠ADC ( 90° ) ( AD bisects ∠A )

Answer:

△ADB ≅ △ADC ( by ASA congruence criterion )

Answer 2

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