Question

In the adjoining figure, ABCD is a
parallelogram, Points. Mand Nare the
midpoints of sides AB and DC
respectively. Then prove that
BP = PQ = QD​

Answer 1

Answer:

PROOF = SINCE ABCD IS A PARALLELOGRAM

THEN AB = CD

=> 1/2 AB = 1/2 CD

=> AM = CN

ALSO AB ll CD

=> AM ll CN

=> AMCN IS A PARALLELOGRAM

=> CM ll AN

NOW IN TRIANGLE BQA

M IS MID POINT OF AB AND PM ll AQ THEN USING CONVERSE OF MID POINT THEOREM

P IS THE MID POINT OF BQ

=> BP=BQ

ANGLE BPC AND ANGLE MPQ ARE EQUAL (VOA)

ANGLE MPQ = AMGLE PQN = ANGLE AQD

CONGRUENT TRIANGLE BPC AND TRIANGLE AQD

=> BP = QD

Answer 2

Answer:

The answer is in this attachment