In ll^gm ABCD,two points PandQ are taken on diagonal BD such that DP=BQ

Show that

a]triangle APD congruent totriangle CQB

b]AP=CQ

c]triangle AQB congruent to triangle CPD

d]AQ=CP

e]APCQ is a ll^gm

We have-

1> In triangle APD and CQB

AD = CB

angle ADP = angle CBQ  (alternate interior angles)

PD = QB  (given)

2> So by corresponding part of congruent triangle-

AP = CQ

3> In triangle AQB and CPD

AB = CD

angle ABQ = angle CDP  (alternate interior angles)

PD = QB  (given)

4> So by corresponding part of congruent triangle-

AQ = CP.

5> Since AP = CQ and AQ = CP

So opposite sides are equal hence APCQ is a ||gm.