A quadrilateral is a parallelogram if a pair of opposite sides is equal and parallel prove?

Answer 1

A quadrilateral is a parallelogram if one pair of opposite sides are equal and parallel

Let ABCD be a quadrilateral in which ABCD and AB=CD, where means parallel to.

Construct line AC and create triangles ABC and ADC.

Now, in triangles ABC and ADC,

AB=CD (given)

AC = AC (common side)

Angle BAC=Angle ACD

(corresponding parts of corresponding triangles or CPCTC)

Triangle ABC is congruent to triangle CDA by Side Angle Side

Angle BCA =Angle DAC by CPCTC

And since these are alternate angles, ADBC.

Thus in the quadrilateral ABCD, ABCD and ADBC.

We conclude ABCD is a parallelogram. var content_characters_counter = '1032';