ABCD is a parallelogram. P and Q are the mid points of sides BC and AD. X and Y are any two points on sides AB and DC. Prove that XY is bisected by PQ at O.
Answers
Answer:
search-icon-header
Search for questions & chapters
search-icon-image
Class 8
>>Maths
>>Understanding Quadrilaterals
>>Parallelogram
>>P and Q are points on oppostie sides AD
Question
Bookmark
P and Q are points on oppostie sides AD and BC of a parallelogram ABCD such that PQ passes through the point of intersection O of its diagonals AC and BD. PQ is bisected at O.
Medium
Solution
verified
Verified by Toppr
Correct option is A)
ABCD is a parallelogram whose diagonals bisect each other at O.
In △ODP and △OBQ,
⇒ ∠BOQ=∠POD [ Vertically opposite angles are equal ]
⇒ ∠OBQ=∠ODP [ Alternate interior angles ]
⇒ OB=OD [ Given ]
∴ △ODP≅△OBQ [ By ASA congruence rule ]
∴ OP=OQ [ By C.P.C.T ]
Hence, PQ is bisected at O.