Ex 8.1, 9
In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP = BQ Show that:
APD CQB
Given: ABCD is a parallelogram
where DP = BQ
To prove: APD CQB
Proof:
Now, AD BC
and transversal BD.
ADP = CBQ
In APD and CQB,
AD = CB
ADP = CBQ
DP = BQ
APD CQB
Ex 8.1, 9
In parallelogram ABCD, two points P and Q are
taken on diagonal BD such that DP = BQ
Show that:
(ii) AP = CQ
In previous part,
we proved that APD CQB,
AP = CQ
Ex 8.1, 9
In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP = BQ Show that:
(iii) AQB CPD
Since,
AB DC
and transversal BD.
ABQ = CDP
In AQB and CPD,
AB = CD
ABQ = CDP
BQ = DP
AQB CPD
Ex 8.1, 9
In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP = BQ. Show that:
(iv) AQ = CP
In previous part,
we proved that AQB CPD,
AQ = CP
Ex 8.1, 9
In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP = BQ. Show that:
(v) APCQ is a parallelogram
In part (ii) & (iv) we proved that
AP = CQ
and
AQ = CP
Since both pairs of opposite sides in APCQ are equal,
APCQ is a parallelogram.

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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