Question

In the figure, if angle AED = angle BDC angle BAE then show that AB||CD

Answer 1

AB || CD

Hence proved

Step-by-step explanation:

In the adjoining figure, (attachment )

Given: ∠AED = ∠BDC + ∠BAE

To prove: AB || CD

In ΔABE, ∠AED is an exterior angle.

∠AED = ∠ABE + ∠BAE     ( Exterior angle theorem)

Exterior angle theorem: Sum of two opposite interior angle is equal to corresponding exterior angle.

But ∠AED = ∠BDC + ∠BAE   ( Given )

Therefore, ∠ABE = ∠BDC

∠ABE = ∠BDC   (Alternate interior angle)

If AB || CD and  BD is traversal line.

Alternate Interior Angle: If two lines are parallel and one traversal line cut both line then two interior opposite angles are equal.

AB || CD

Hence proved

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Answer 2

Answer:

Step-by-step explanation:

<AED=<ABE+<BAE (exterior angles)

<AED=<BDC+<BAE( given)

<ABE=<BDC

<ABE=<BDC (alteranate interior angles)

AB//CD

HENCE PROVED