Question

Mid points of opposite sides of a parallelogram are joined as shown in the figure 11 21 that Show (1) AD || PQ (1) APQD is a parallelogram (ii) ABSR is a parallelogram (iv) APOR is a parallelogram Q Fig. 11.21​

Answer 1

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In the adjacent figure ABCD is a parallelogram P,Q are the midpoints of sides AB and DC respectively. Show that PBCQ is also a parallelogram

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Solution

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Since AB∥CD [ Opposite sides of ∥

gm

are parallel ]

⇒PB∥QC [ Parts of parallel lines are parallel ]

Also, AB=CD [ Opposite sides of ∥

gm

are equal ]

⇒

2

1

AB=

2

1

CD

⇒PB=QC [ P is the mid point of Ab and Q is the mid point of DC ]

Since PB∥QC and PB=QC

One pair of opposite sides of PBCQ are equal and parallel.

∴PBCQ is a ∥

gm

.