Elements of a Parallelogram

Q. Find the values of x and y in the following parallelogram.

1. x = 3
   y = 4
2. x = 6
   y = 6
3. x = 4
   y = 3
4. x = 5
   y = 8

Q.

$\text{In parallelogram ABCD, X and Y are mid-points of opposite sides AB and DC respectively. Prove that :}\left(i\right)AX=YC\left(ii\right)AX\text{is parallel to YC}\left(iii\right)\text{AXCY is a parallelogram.}$

Q.

Prove that the point of intersection of the two diagonals of a parallelogram is the midpoint of both the diagonals.

Q.

Two adjacent sides ofa a parallelogram are 4 cm and 3 cm respectively. Find its perimeter.

Q. Two consecutive sides of a parallelogram are 4x+5y=0 and 7x+2y=0.if the equation of one diagonal is11x+7y=9 find the equation of the other diagonal.

Q.

All the angles of a quadrilateral are equal to each other. Find the measure of each. Is the quadrilateral a parallelogram ?
What special type of parallelogram is it?

Q.

The shorter side of a parallelogram is 4.8 cm and the longer side is half as much again as the shorter side. Find the perimeter of the parallelogram.

Q. ABCD is a parallelogram. Which of the following is not true about ABCD?

1. $AB=CD$
2. $AD=CB$
3. $AD||CD$
4. $AB||CD$

Q.

When two straight lines intersect, which of the following statements are true?

1. (i) and (iii) are correct
2. (ii) and (iii) are correct
3. (i) and (iv) are correct

4. (ii) and (iv) are correct

Q. Question 2 (v)
Consider the following parallelograms. Find the values of the unknowns x, y, z
(v)

Q. Two adjacent angles of a parallelogram are congruent what is the measure of each

Q. Tick (✓) the correct answer:
The diagonals do not necessarily bisect the interior angles at the vertices in a
(a) rectangle
(b) square
(c) rhombus
(d) all of these

Q.

$\text{In parallelogram ABCD, E is the mid-point of AD and F is the mid-point of BC. Prove that BFDE is a parallelogram.}$

Q.

If ABCD is a parallelogram, then the angle bisectors of $\angle A$ and $\angle D$ meet at ‘O’. The measure of $\angle AOD$ is ${45}^{\circ }$​

1. True

2. False

Q. Question 10

Ratio of area of $\Delta MNO$ to the area of parallelogram MNOP in the given figure.


(a) 2 : 3
(b) 1 :1
(c) 1 : 2
(d) 2 : 1

Q.

ABCD is a parallelogram. The sides AB and AD are produced to E and F respectively, such that $\mathrm{AB}=\mathrm{BE}$ and $\mathrm{AD}=\mathrm{DF}$.

Prove that $△\mathrm{BEC}\cong △\mathrm{DCF}$.

Q.

The difference between the two adjacent angles of a parallelogram is 20°. Find measures of all the angles of the parallelogram.

Q. Define quadrilateral ?

Q.

In the figure, BDEF and DCEF are each a parallelogram, It is true that BD = DC?
Why or Why not?

Q. Question 175
A line l is parallel to line m and a transversal p intersects them at X, Y respectively. Bisectors of interior angles at X and Y intersect at P and Q. Is PXQY a rectangle? Give reason.

Q.

Diagonals of parallelogram ABCD intersect at O as shown in the figure. XY contains O, and X, Y are points on opposite sides of the parallelogram. Give reasons for each of the following :

(i) OB = OD
(ii) $\angle OBY=\angle ODX$
(iii) $\angle BOY=\angle DOX$
(iv) $\Delta BOY\cong \Delta DOX$
Now, state if XY is bisected at O.

Q.

Assume line "m" and line "n" are parallel lines that are cut by the transversal line "l." Find the value of "x."

1. $x={25}^{\circ }$
2. $x={45}^{\circ }$
3. $x={15}^{\circ }$
4. $x={35}^{\circ }$

Q.

In parallelogram ABCD, which of the 2 sides are equal?

1. AB & AD

2. AB & BC

3. CD & BC

4. AB & CD

Q.

In the figure, ABCD is a parallelogram and AB = 6 cm. If the area of triangle ADE is $\frac{3}{4}$ that of parallelogram ABCD, find the length of BE. [1 MARK]

Q.

The adjacent angles of a parallelogram are in the ratio 2:1. Find the measures of all the angles.

Q. Explain why a rectangle is a convex quadrilateral.

Q.

A trapezium is a quadrilateral with

1. two pairs of equal consecutive sides.

2. a pair of parallel sides.

3. two pairs of parallel sides.

4. two equal sides.

Q.

An octagon is made up of ______ sides.

1. 8

2. 10

3. 6

4. 5

Q.

Name the quadrilaterals whose diagonals.

(i) bisect each other

(ii) are perpendicular bisectors of each other

(iii) are equal

Q. Question 1 (i)
Given a parallelogram ABCD. Complete each statement along with the definition or property used.
(i) AD = ..........