Advertisements
Advertisements
प्रश्न
ABCD is a parallelogram. P and Q are mid-points of AB and CD. Prove that APCQ is also a parallelogram.
Advertisements
उत्तर
In quandrilateral APCQ,
AP || QC ...(since AB || CD)
AP = `(1)/(2)"AB"` ...(given)
CQ = `(1)/(2)"CD"` ...(given)
But AB = CD
⇒ AP = CQ
Therefore, APCQ is a parallelogram.
संबंधित प्रश्न
ABCD is a rectangle with ∠ADB = 55°, calculate ∠ABD.
PQRS is a parallelogram. T is the mid-point of RS and M is a point on the diagonal PR such that MR = `(1)/(4)"PR"`. TM is joined and extended to cut QR at N. Prove that QN = RN.
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.
PQRS is a parallelogram and O is any point in its interior. Prove that: area(ΔPOQ) + area(ΔROS) - area(ΔQOR) + area(ΔSOP) = `(1)/(2)`area(|| gm PQRS)
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"`.
