Question

p and q are mid point of side AB and CD of a parallelogram ABCD prove that APCQ is a parallelogram.​

Answer 1

Answer:

APCQ is a parallelogram. In quadrilateral APCQ, QC and AP is parallel and equal(Half of DC and AB). Hence, APCQ is a parallelogram

Answer 2

Answer:

AB = CD (opposite sides of a parallelogram are equal in length)

½AB = ½CD

AP = PB = ½AB (Given: P is the midpoint of side AB)

CQ = QD = ½CD (Given: Q is the midpoint of side CD)

Therefore, AP = CQ

AB || CD (opposite sides of a parallelogram are parallel to each other)

AP on AB and CQ on CD

Therefore, AP || CQ

As opposite sides of the quadrilateral APCQ are equal(AP = CQ) and are parallel to each other(AP||CQ) APCQ is a parallelogram.