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प्रश्न
Prove that the bisectors of the base angles of an isosceles triangle are equal.
बेरीज
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उत्तर
An isosceles triangle △ABC with AB = AC
Let:
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AD be the bisector of angle ∠B
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AE be the bisector of angle ∠C
Length of AD = Length of AE
In △ABD and △ACE:
AB = AC ...(Given)
∠ABD = ∠ACE ...(Each is half of equal base angles)
∠ADB = ∠AEC ...(Vertically opposite angles)
By ASA (Angle-Side-Angle) congruence:
△ABD ≅ △ACE ⇒ AD = AE
Proved: AD = AE
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