Opposite Sides in a Parallelogram Are Equal

Q. 28. ABCD is a parallelogram and X and Y are the mid-points of BC and CD respectively. Prove that ar(Δ AXY)=3/8 ar(||gm ABCD).

Q.

If BDEF and FDCE are parallelograms, then

___ lies equidistant to points B and C. (Fill in one among A/F/E/D).

Q. ABCD is a trapezium in which AB|| DC, DC=30cm and AB=50cm. If X and Y are respectively the mid-points of AD and BC, then prove that ar(DCYX)=7/9ar(XYBA)

Q.

In the figure below, ABCD is a parallelogram and X, Y are the midpoints of AB, CD. The lines DX and BY cut AC at P and Q.

Prove that AP = PQ = QC.

Q.
If ABCD is a quadrilateral in which P.Q, R and S are mid-points of the sides AB, BC, CD and DA ( see the given figure). AC is a diagonal. Then, PQRS is also a parallelogram. (T/F)

1. True
2. False

Q. In the adjacent figure, ABCD is a parallelogram and the line segments AE and CF bisect the angles A and C respectively. Show that AE=CF

Q. ABCD is a parallelogram, E and F are the mid-points of AB and CD respectively. GH is any line intersecting AD, EF and BC at G, P and H respectively. Prove that GP = PH.

Q.

A quadrilateral having two pairs of parallel sides is

1. polygon

2. hexagon

3. parallelogram

4. trapezoid

Q.

D, E, F are respectively the mid points of the sides BC, CA, AB of triangle ABC. Then CEFD is definitely a parallelogram.

1. Rectangle

2. Parallelogram

3. Trapezium

4. Rhombus

Q.

A quadrilateral is a parallelogram, if pair of opposite sides are equal and __.

Q.

If BDEF and FDCE are parallelograms, then

___ lies equidistant to points B and C. (Fill in one among A/F/E/D).

Q. In a parallelogram, PQRS, $PR\ne QSandPR\pm QS$. Then PQRS is a

1. rhombus
2. square
3. parallelogram
4. trapezium

Q. $P$ is a point in the interior of a parallelogram $ABCD$. Show that $ar\left(△APB\right)+ar\left(△PCD\right)=\frac{1}{2}ar\left(ABCD\right)$

Q. ntABCD is a parallelogram and P is the mid point of BC. Prove that AC and DP meet in a common point of trisect.n

Q. In the figure, ABCD is a parallelogram such that $AF$ and $CE$ are the bisectors of $\angle DAB$ and $\angle BCD$ respectively, then $AF\parallel CE$.

1. True
2. False