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Question
Fill the blank in the following so that the following statement is true.
In an isosceles triangle ABC with AB = AC, if BD and CE are its altitudes, then BD is …… CE.
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Solution
In an isosceles triangle ABC with AB AC, if BD and CE are its altitudes, then BD
is equal to CE
Reason: Since angles opposite to equal sides are equal, so
∠ABC=∠ ACB
⇒∠EBC=∠ DCB
So, by ASA congruence criterion
ΔEBC ≅ ΔDCB
⇒CE = BD [Corresponding parts of congruent
triangles are equal]
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