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Question

Suppose ABC is an isosceles triangle with AB=AC ; BD and CE are bisectors of B and C. Prove that BD=CE

Solution
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In ABC
AB=AC [Given]
ABC=ACB......(1) [Angles opposite to equal sides of a trinagle are equal]
Also, 12AB=12AC
BE=CD.......(2) [Halves of equals are equal]
Since BD and CE are two medians
Now,
In BDC and CEB
From (1) BCD=CBE
From (2) BE=CD
BC=CB [Common]
BDCCEB [SAS Congruence rule]
BD=CE [By CPCT]

1078931_1184022_ans_2921ed32f89241d2ad7c9abb72d52944.png

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