Show that the line segment joining …
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Yogita Ingle 4 years, 5 months ago
In △ADC,S is the mid-point of AD and R is the mid-point of CD
In △ABC,P is the mid-point of AB and Q is the mid-point of BC
Line segments joining the mid-points of two sides of a triangle is parallel to the third side and is half of of it.
∴SR ∥ AC and SR= 1/2 AC ....(1)
∴PQ ∥ AC and PQ= 1/2 AC ....(2)
From (1) and (2)
⇒ PQ = SR and PQ ∥ SR
So,In PQRS,
one pair of opposite sides is parallel and equal.
Hence, PQRS is a parallelogram.
PR and SQ are diagonals of parallelogram PQRS
So,OP=OR and OQ=OS since diagonals of a parallelogram bisect each other.
Hence proved
1Thank You