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.

Made by

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.