Question

Given: AD = BC and AD || BC

Answer 1

Answer:

ABCD is a parallelogram.

Step-by-step explanation:

A parallelogram is a quadrilateral that has two parallel and equal pairs of opposite sides.    

From the given diagram,

Given: AD = BC and AD || BC, then:

i. AB = DC (both pairs of opposite sides of a parallelogram are congruent)

ii. <ADC = < BCD and < DAB = < CBA

thus, AD || BC and AB || DC (both pairs of opposite sides of a parallelogram are parallel)

iii. < BAC = < DCA (alternate angle property)

iv. Join BD, line AC  and BC are the diagonals of the quadrilateral which bisect each other. The two diagonals are at a right angle to each other.

v. <ADC + < BCD + < DAB + < CBA = $360^{0}$  (sum of angles in a quadrilateral equals 4 right angles)

Therefore, ABCD is a parallelogram.