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Question

In the given figure, ray AE bisects exterior CAD and ray AE is parallel to side BC. Hence, AB=AC.
State whether the above statement is true or false.
194745_612cb702e4ff45fda079c494d0f15bef.png

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Solution

Given, AEBC
hence, EAC=ACB ...(Alternate angle to parallel lines)
Also, DAE=ABC ....(Corresponding angles of parallel lines)
We know, AE bisects DAC
EAC=DAE
thus, ACB=ABC
ABC is an isosceles triangle

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