Question

an isosceles triangle in which AB=AC AD bisects exterior angle EAC
If CD||AB, show that..
(i) angle DAC=angle BCA
(ii) ABCD is a parallelogram
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Answer 1

Answer:

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Answer 2

Answer:

Given : AB = AC

CD ║AB

To prove : ΔBCA ≅ ΔDAC

and ABCD is parallelogram , i.e, One pair of opposite arms is parallel and equal. So, it is enough to prove AB = CD.

Proof:

Consider ΔDAC and ΔBCA

∠DAC = ∠BCA (Alternate angles)

AC = CA (Common)

∠DCA = ∠BAC (Alternate angles)

∴ΔDAC ≅ ΔBCA by ASA Congruence condition.

Since the triangles are congruent, we have

BC = AD ,

AB = CD and

∠ABC = ∠ADC

Since, AB = CD and AB ║CD, ABCD is a parallelogram.

Hence proved.

Step-by-step explanation: