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Given:-
AD is the bisector of ∠A So we have, ∠DAB = ∠DAC
(1) AD ⊥BC
So we have, ∠BDA = ∠CDA = 90o
To prove,
ΔABC is isosceles. Proof, In ΔDAB and ΔDAC, ∠BDA = ∠CDA = 90o DA = DA (common) ∠DAB = ∠DAC (from 1) By ASA congruence property, ΔDAB ≅ ΔDAC AB = AC
Hence,
ΔABC is isosceles. !!!
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Answer:
Given:-
AD is the bisector of ∠A So we have, ∠DAB = ∠DAC
(1) AD ⊥BC
So we have, ∠BDA = ∠CDA = 90o
To prove,
ΔABC is isosceles. Proof, In ΔDAB and ΔDAC, ∠BDA = ∠CDA = 90o DA = DA (common) ∠DAB = ∠DAC (from 1) By ASA congruence property, ΔDAB ≅ ΔDAC AB = AC
Hence,
ΔABC is isosceles. !!!
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