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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.
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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