Advertisements
Advertisements
Question
In a parallelogram PQRS, M and N are the midpoints of the opposite sides PQ and RS respectively. Prove that
MN bisects QS.
Advertisements
Solution
M and N are the mid-points of PQ and RS respectively.
⇒ MN || QR
Let MN intersect QS at point O.
We know that the segment drawn through the mid-point of one side of a triangle and parallel to the other sides bisects the third side.
In ΔSRQ, N is the mid-point of RS and ON || QR
∴ O is the mid-point of SQ
⇒ OQ = OS ....(iii)
⇒ ON bisects QS
⇒ MN bisects QS.
APPEARS IN
RELATED QUESTIONS
ABCD is a rectangle with ∠ADB = 55°, calculate ∠ABD.
P is a point on side KN of a parallelogram KLMN such that KP : PN is 1 : 2. Q is a point on side LM such that LQ : MQ is 2 : 1. Prove that KQMP is a parallelogram.
Prove that the line segment joining the mid-points of the diagonals of a trapezium is parallel to each of the parallel sides, and is equal to half the difference of these sides.
In a parallelogram PQRS, M and N are the midpoints of the opposite sides PQ and RS respectively. Prove that
PMRN is a parallelogram.
In the given figure, PQRS is a parallelogram in which PA = AB = Prove that: SA ‖ QB and SA = QB.
Prove that the diagonals of a kite intersect each other at right angles.
Prove that the diagonals of a parallelogram divide it into four triangles of equal area.
In the given figure, AB ∥ SQ ∥ DC and AD ∥ PR ∥ BC. If the area of quadrilateral ABCD is 24 square units, find the area of quadrilateral PQRS.
In ΔPQR, PS is a median. T is the mid-point of SR and M is the mid-point of PT. Prove that: ΔPMR = `(1)/(8)Δ"PQR"`.
The medians QM and RN of ΔPQR intersect at O. Prove that: area of ΔROQ = area of quadrilateral PMON.
