Question

10. Prove that ABC is an isosoles, if Altitude AD bisects angleBAC​

Answer 1

Step-by-step explanation:

In ΔABC, let the altitude AD bisects ∠BAC

Then we have to prove that the ΔABC is isosceles.

In triangle ADB and ADC,

∠BAD=∠CAD (AD is bisector of ∠BAC)

AD=AD (common)

∠ADB=∠ADC (Each equal to 90

o

)

⇒ΔADB≅ΔADC (by ASA congruence criterion)

⇒AB=AC (cpct)

Hence, ΔABCis an isosceles.