Question

In triangle ABC, AD is the bisector of ZA. If ADI BC, prove that AB = AC.​

Answer 1

Answer:

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Step-by-step explanation:

Given in ΔABC, the bisector AD of ∠A is perpendicular to side BC.

Given in ΔABC, the bisector AD of ∠A is perpendicular to side BC.In ΔBAD and ΔCAD, 

Given in ΔABC, the bisector AD of ∠A is perpendicular to side BC.In ΔBAD and ΔCAD, ∠BAD=∠CAD    —Given

Given∠ADB=∠ADC=900 —(AD is  perpendicular to side BC)

(AD is  perpendicular to side BC)AD=AD —(Common side)

(Common side)∴ΔBAD≅ΔCAD   —[ASA test]

[ASA test]∴AB=AC      —[CSCT]

(hence proved)

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