Question

ABCD is a quadrilateral in which all the four angles are equal. Show that AB || CD
and AD || BC​

Answer 1

ABCD is a quadrilateral in which AB=BC=CD=DA.

To prove:- AB | | CD. and. BC | | AD.

Construction:- join A to. C.

Proof:- In ∆ ABC and ∆ ADC

AB. = DC. (given)

BC. = AD. (given)

AC. = AC. (common in both triangles )

∆ABC congruence ∆ADC.

Therefore. Angeles BAC = angle DCA. (Alternate angles ) and AB | | CD.

Also angle BCA = angle. DAC. (Alternate angles). and. BC | | AD. Proved.