Parallelogram

Q.

ABCD is a parallelogram in which $\angle ={110}^{\circ }$. Find the measure of each of the angles $\angle B,\angle Cand\angle D$.

Q.

If one angle of a parallelogram is ${24}^{\circ }$ less than twice the smallest angle then the largest angle of the parallelogram is

(a) ${68}^{\circ }$ (b) ${102}^{\circ }$

(c) ${112}^{\circ }$ (d) ${176}^{\circ }$

Q.

The opposite sides of a rectangle are:

1. Equal

2. Parallel

3. Unequal

4. Both A and B

Q.

Diagonals are of equal length in

1. Square and rhombus

2. Rectangle and square

3. Kite and rhombus

4. Rhombus and rectangle

Q.

Prove that the sum of the squares of the sides of rhombus is equal to the sum of the squares of its diagonals.

Q. the ratio of two sides of a parallelogram is 4:3. if its perimeter is 56 cm find the length of its side.

Q.

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

Q. Question 178
The angle between the two altitudes of a parallelogram through the vertex of an obtuse angle of the parallelogram is ${45}^{\circ }$. Find the angles of the parallelogram.

Q.

Two sides of a parallelogram are in the ratio 5 :3 If its perimeter is 64 cm, find the length of its sides.

Q.

All rectangles are parallelograms, but all parallelograms are not rectangles. Justify this statement.

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

1. 3 cm
2. 7 cm
3. 14 cm
4. 12 cm

Q.

Shorter side of a parallelogram is 3.6cm and longer side is half than shorter side. Find perimeter of parallelogram.

Q.

Which of the following statements are true and which are false

(i) The diagonals of a parallelogram are equal.

(ii) The diagonals of a rectangle are perpendicular to each other.

(iii) The diagonals of a rhombus are equal.

(iv) Every rhombus is a kite.

(v) Every rectangle is a square.

(vi) Every square is a parallelogram.

(vii) Every square is a rhombus.

(viii) Every rectangle is a parallelogram.

(ix) Every parallelogram is a rectangle.

(x) Every rhombus is a parallelogram.

Q. Which of the following statements are true and which are false?
(i) The diagonals of a parallelogram are equal.
(ii) The diagonals of a rectangle are perpendicular to each other.
(iii) The diagonals of a rhombus are equal.
(iv) Every rhombus is a kite.
(v) Every rectangle is a square.
(vi) Every square is a a parallelogram.
(vii) Every square is a rhombus.
(viii) Every rectangle is a parallelogram.
(ix) Every parallelogram is a rectangle.
(x) Every rhombus is a parallelogram.

Q. In the given figure, if ABCD is a parallelogram then find the value of x, y and z (in degrees).

(4 marks)

Q. Consider the following parallelograms. Find the values of the unknowns $x,y,z$

Q. In the given figure, $ABCD$ is the parallelogram, $AO$ and $BO$ are the angle bisectors of $\angle A$ and $\angle B$.

find $\angle AOB$.

1. Greater than ${90}^o$
2. Less than ${90}^o$
3. ${90}^o$
4. ${60}^o$

Q.

If consecutive sides of a parallelogram are equal, then its necessarily a ____

Q. Question 115
State whether the statements are True or False.
Every parallelogram is a rectangle.

Q.

State whether True or False.

(a) All rectangles are squares.

(b) All rhombuses are parallelograms.

(c) All squares are rhombuses and also rectangles.

(d) All squares are not parallelograms.

(e) All kites are rhombuses.

(f) All rhombuses are kites.

(g) All parallelograms are trapeziums.

(h) All squares are trapeziums.

Q.

The perimeter of parallelogram $\text{ABCD}$ is equal to $10\text{cm}$. Find the length of diagonal $\text{BD}$ if you know that the perimeter of $△\text{ABD}$ is $8\text{cm}$.

Q. Opposite sides of a parallelogram are parallel, but not equal.

1. False
2. True

Q.

There is a parallelogram inside a circle such that all of its vertices lie on the circle. Which of the following can be true for the parallelogram in this case?

i) It can be a rhombus

ii) It can be a square

iii) It can be a rectangle

(iv) It can be trapezium

1. ii, iii, iv

2. All of these

3. i , ii

4. ii, iii

Q. If two parallel lines are cut by a traversal, then alternate interior angles are and co-interior angles are

1. equal
2. unequal
3. supplementary
4. complementary

Q.

Question 1 (g)
State whether true or false.

(g) All parallelograms are trapeziums.

Q.

If ABCD is a parallelogram then:

1. AB is parallel to CD

2. CD is parallel to DA

3. AB is parallel to BC

4. AB is parallel to AC

Q. Question 4
For which of the following, diagonals are perpendicular to each other?
a) Parallelogram
b) Kite
c) Trapezium
d) Rectangle

Q. Question 176
ABCD is a parallelogram. The bisector of angle A intersects CD at X and bisector of angle C intersects AB at Y. Is AXCY a parallelogram? Give reason.

Q.

A rectangle has ______ equal diagonals.

1. 4

2. 1

3. 2

4. 3

Q. A rhombus is a parallelogram with all the sides equal and opposite interior angles equal as well.

1. True
2. False