Question

In the figure given below AB=AC angle EAD =angle CAD and CD is parallel to AB show that ABCD is a parallelogram

Answer 1

Answer:

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Answer 2

Answer:

ABCE is a parallelogram

AB=AC⇒∠ABC=∠ACB

Let \angle ABC = \angle ACB = x$$

∠BAC=180°−2x [Angle sum property]

AB∥CE⇒∠BAC=∠ACE

∠BAC=∠ACE=(180°−2x)

∠BAC+∠EAC+∠EAD=180° [Linear Pair]

(180°−2x)+2∠EAC=180°

2∠EAC=2x

∠EAC=x

Therefore, ∠EAC=∠ACB

∠EAC=∠ACB⇒AE∥BC

Therefore, ABCE is a parallelogram.

Step-by-step explanation:

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