Question

ABCD is a quadrilateral in which all four sides are equal. Show that both pairs
opposite sides are parallel.
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Answer 1

Answer:

Step-by-step explanation:

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.