Ex 8.2, 1
ABCD is a quadrilateral in which P, Q, R and S are mid-points of the sides AB, BC, CD and DA. AC is a diagonal. Show that :
SR ∥ AC and SR =1/2 AC
Given: ABCD is quadrilateral where
P, Q, R and S are mid-points of the sides
AB, BC, CD and DA respectively
To prove: SR ∥ AC and SR = 1/2 AC
Proof:
In ΔADC,
S and R are the mid-points of sides AD and CD respectively.
∴ SR ∥ AC and SR = 1/2 AC
Ex 8.2, 1
ABCD is a quadrilateral in which P, Q, R and S are mid-points of the sides AB, BC, CD and DA. AC is a diagonal. Show that :
(ii) PQ = SR
In previous part we proved,
SR ∥ AC and SR = 1/2 AC
In ΔABC,
P and Q are mid-points of sides AB and BC respectively.
PQ ∥ AC and PQ = 1/2 AC
From (1) & (2)
⇒ PQ = SR & PQ ∥ SR
Hence proved
Ex 8.2, 1
ABCD is a quadrilateral in which P, Q, R and S are mid-points of the sides AB, BC, CD and DA. AC is a diagonal. Show that :
(iii) PQRS is a parallelogram.
In previous part we proved
PQ = SR
Also, we proved
PQ ∥ AC & SR ∥ AC
So, PQ ∥ SR
In PQRS,
one pair of opposite sides of is parallel and equal.
Hence, PQRS is a parallelogram.

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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