Question

А
BQ
D
Р
(see Fig. 8.20). Show that:
(1) A APD=ACQB
(i) AP=CQ
(iii) AAQB=A CPD
(iv) AQ=CP
B
C С
(v) APCQ is a parallelogram
Fig. 8.20
9. In parallelogram ABCD, two points P and Q are
taken on diagonal BD such that DP

PLEASE ANSWER ME FAST​

Answer 1

Answer:

given that ABCD is parallelogram and P&Q are points on BD such that DP=BQ

to prove -I) , ii), iii) iv) v) I am not writing full you just write all points from question

proof-ABCD is parallelogram so opposite sides equal and alternate angle are equal.

in APD and CQB

PD = CB (given)

angle QBC = angle PDA ( alternate angle of side AD and BC)

AD = BC ( opposite sides of parallelogram)

so, both triangle are congruent by SAS congruency rule

therefore by cpct

AP = CQ

in AQB and CPD

BQ= DP (given)

AB= CD ( opposite sides of parallelogram)

angle ABQ = angel CDP (alternate angles)

so both triangle are congruent by SAS congruency rule

therefore by cpct

AQ=CP

AP= CQ and AQ = CP

opposite sides are equal in quadrilateral APCQ so,

APCQ is parallelogram...

hope you understand...