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Question 2
In figure, D and E are points on side BC of the a ΔABC such that BD = CE and AD = AE, show that ΔABDΔAE show that ΔABDΔACE

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Solution

Given D and E are the points on side BC of a such that BD = CE and AD = AE to show ΔABDΔACE
proof we have AD =AE [given]
ADE=AED....(i)
[since, angles opposite to equal sides are equal]
we have ADB+ADE=180 [linear pair axiom]
ADB=180ADE
=180AED [from Eq.(i)]
in ΔABD and ΔACE
ADB=ACE[AEC+AED=180, linear pair axiom]
BD =CE [Given]
and AD =AE [Given]
ΔBDΔACE [by SAS congruence rule]

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