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 parallelogram. P and T are points on AB and DC respectively and AP = CT. Prove that PT and BD bisect each other.
PQRS is a parallelogram. PQ is produced to T so that PQ = QT. Prove that PQ = QT. Prove that ST bisects QR.
ABCD is a rectangle with ∠ADB = 55°, calculate ∠ABD.
Prove that if the diagonals of a parallelogram are equal then it is a rectangle.
In a parallelogram PQRS, M and N are the midpoints of the opposite sides PQ and RS respectively. Prove that
RN and RM trisect QS.
ABCD is a trapezium in which side AB is parallel to side DC. P is the mid-point of side AD. IF Q is a point on the Side BC such that the segment PQ is parallel to DC, prove that PQ = `(1)/(2)("AB" + "DC")`.
Prove that the diagonals of a square are equal and perpendicular to each other.
In the given figure, PQ ∥ SR ∥ MN, PS ∥ QM and SM ∥ PN. Prove that: ar. (SMNT) = ar. (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"`.
In the figure, ABCD is a parallelogram and CP is parallel to DB. Prove that: Area of OBPC = `(3)/(4)"area of ABCD"`
