Question

62. In the figure, given below, ABCD is a
trapezium in which AB//DC, P is mid-point
of AD and Q is mid-point of BC.
(i) Write a relation connecting AB, PQ and
DC.
(ii) Find DC, if AB = 16 cm and PQ = 23
cm.
А
B
P
Q
#
D
C​

Answer 1

Step-by-step explanation:

In △, BDC and BQR,

∠B=∠B (Common)

∠BDC=∠BQR (Corresponding angles of parallel lines)

∠BCD=∠BRQ (Corresponding angles of parallel lines)

thus, △BDC∼△BQR

Thus,

QB

BD

=

QR

DC

2=

QR

DC

(Q is the mid point of BD)

QR=

2

1

DC

Similarly, QP=

2

1

AB

Hence, QR+QP=

2

1

(AB+DC)

PR=

2

1

(AB+CD)