Question

9. A parallelogram ABCD has P the mid-point
of DC and Q a point of AC such that
D
Р
>
Q
1
AC. PQ produced meets BC at R.
CQ =
4
Prove that :
(i) R is the mid-point
of BC,
1
(ii) PR =
DB.
2
А
B
R​

Answer 1

ǫᴜᴇsᴛɪᴏɴ -

A parallelogram ABCD has P the mid-point of DC and Q a point of AC such that CQ = 1/4 AC. PQ produced meets BC at R.

Prove that :

(i) R is the midpoint of BC,

(ii) PR = 1/2 DB.

ɢɪᴠᴇɴ -

• ABCD is a parallelogram.
• P and Q are the mid-point of DC and AC respectively.
• CQ = 1/4 AC.

Tᴏ ᴘʀᴏᴠᴇ -

1. R is the mid-point of BC,
2. PR = 1/2 DB.

ᴘʀᴏᴏғ -

In ∆ DCB,

P is the midpoint of AC.

∴ PR bisects side CB.

∴ CR = RB.

∴ R is the midpoint of BC.

______________________(proved)

And,

PR = 1/2 DB ________(mid-point theorem)

_____________________(proved)

@MissSolitary✌️

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