Proving opposite sides of a parallelogram are congruent

Question

Given: ABCD is a parallelogram
Prove: Segment AB ≅ Segment CD,
Segment BC ≅ Segment AD

Answer 1

 

Draw the diagonal from A to C.

 

Because of the parallel sides, angle BAC and angle DCA are congruent

 

Because of the parllel sides, angle BCA and angle DAC are concongruent

 

AC is equal to itself by reflexive property

 

So triangle BAC and trangle DCA are congruent by ASA

 

AB = CD and AD = BC by CPCTC