Advertisements
Advertisements
Question
ABCD is a quadrilateral P, Q, R and S are the mid-points of AB, BC, CD and AD. Prove that PQRS is a parallelogram.
Advertisements
Solution
Join AC and BD
In ΔABC,
P and Q are mid-point of AB and BC respectively.
Therefore, PQ || AC and PQ = `(1)/(2)"AC"` ........(i)
In ΔADC,
S and R are mid-point of AD and DC respectively.
Therefore, SR || AC and SR = `(1)/(2)"AC"` ........(ii)
From (i) and (ii)
PQ || SR and PQ = SR
Therefore, PQRS is a parallelogram.
RELATED QUESTIONS
SN and QM are perpendiculars to the diagonal PR of parallelogram PQRS.
Prove that:
(i) ΔSNR ≅ ΔQMP
(ii) SN = QM
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.
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.
In the given figure, PQRS is a parallelogram in which PA = AB = Prove that: SAQB is a parallelogram.
In the given figure, PQRS is a trapezium in which PQ ‖ SR and PS = QR. Prove that: ∠PSR = ∠QRS and ∠SPQ = ∠RQP
Prove that the diagonals of a kite intersect each other at right angles.
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 the figure, ABCD is a parallelogram and CP is parallel to DB. Prove that: Area of OBPC = `(3)/(4)"area of ABCD"`
