Question

29. In a parallelogram PQRS, PQ = 9 cm and PS =5 cm. The bisector of ZP meets SR in A. PA and QR produced meet at B. Then, the length of RB is (a) 5 cm (b) 4 cm (c) 9 cm (d) 6​

Answer 1

Answer:

From the figure we know that PM is the bisector of ∠P

so we get

∠QPM=∠SPM....(1)

We know that PQRS is a parallelogram

from the figure we know that PQ∥SR and PM is a transversal ∠QPM and ∠PMS are alternate angles

∠QPM=∠PMS....(2)

Consider equation (1) and(2)

∠SPM=∠PMS.....(3)

We know that the sides opposite to equal angles are equal

MS=PS=9cm

∠RMT and ∠PMS are vertically opposite angles

∠RMT=∠PMS.....(4)

We know that PS∥QT and PT is the transversal

∠RTM=∠SPM

it can be written as

∠RTM=∠RMT

we know that the sides opposite to equal angles are equal

TR=RM

we get

RM=SR−MS

by substituting the values

RM=12−9

RM=3m

RT=RM=3cm

therefore length of RT is 3cm