The lengths of the diagonals of a rhombus are $16\ cm$ and $12\ cm.$ The length of each side of the rhombus is:
- A$8\ cm$
- B$9\ cm$
- ✓$10\ cm$
- D$12\ cm$
Answer: C.
View full solution →Question types
Parallelograms question types
57 questions across 6 question groups — pick any mix to generate a MATHS paper with step-by-step answer keys.
57
Questions
6
Question groups
5
Question types
01
M.C.Q. [1 Marks Each]
20 Q→02Assertion (A) & Reason (B) MCQ
8 Q→032 Marks Questions
3 Q→043 Marks Question
9 Q→05Case study (4 Marks)
1 Q→061 Marks Question
16 Q→Sample Questions
Parallelograms questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
The two diagonals are not necessarily equal in a:
- ARectangle.
- BSquare.
- ✓Rhombus.
- DIsosceles trapezium.
Answer: C.
View full solution →If an angle of a parallelogram is two-thirds of its adjacent angle, the smallest angle of the parallelogram is:
- A$54^\circ$
- ✓$72^\circ$
- C$81^\circ$
- D$108^\circ$
Answer: B.
View full solution →The length and breadth of a rectangle are in the ratio $4 : 3.$ If the diagonal measures $25\ cm$ then the perimeter of the rectangle is:
- A$56\ cm$
- B$60\ cm$
- ✓$70\ cm$
- D$80\ cm$
Answer: C.
View full solution →Two adjacent angles of a parallelogram are $(2x + 25)^\circ $ and $(3x - 5)^\circ $. The value of $x$ is:
- A$28$
- ✓$32$
- C$36$
- D$42$
Answer: B.
View full solution →Assertion (A): A triangle can have at the most one obtuse angle while a quadrilateral can have at the most three obtuse angles.
Reason ( $R$ ): The sum of the angles of a triangle is $180^{\circ}$ while the sum of the angles of a quadrilateral is $360^{\circ}$.
Reason ( $R$ ): The sum of the angles of a triangle is $180^{\circ}$ while the sum of the angles of a quadrilateral is $360^{\circ}$.
- ABoth A and R are true and R is the correct explanation of A
- BBoth A and R are true but R is not the correct explanation of A
- CA is true but R is false
- DA is false but R is true
Assertion (A): If the diagonals of a quadrilateral bisect each other then it is a parallelogram.
Reason (R): The opposite sides being equal and parallel, a parallelogram is a symmetrical figure and so diagonals bisect each other.
Reason (R): The opposite sides being equal and parallel, a parallelogram is a symmetrical figure and so diagonals bisect each other.
- ABoth A and R are true and R is the correct explanation of A
- BBoth A and R are true but R is not the correct explanation of A
- CA is true but R is false
- DA is false but R is true
Assertion (A): A kite has two pairs of equal adjacent sides but unequal opposite sides.
Reason (R): Every kite is a parallelogram.
Reason (R): Every kite is a parallelogram.
- ABoth A and R are true and R is the correct explanation of A
- BBoth A and R are true but R is not the correct explanation of A
- CA is true but R is false
- DA is false but R is true
Assertion (A): If the diagonals of a quadrilateral are unequal and intersect each other at right angles then it is a parallelogram.
Resson ( $R$ ): Every parallelogram is a trapezium
Resson ( $R$ ): Every parallelogram is a trapezium
- ABoth A and R are true and R is the correct explanation of A
- BBoth A and R are true but R is not the correct explanation of A
- CA is true but R is false
- DA is false but R is true
Assertion (A): In a square $A B C D$, the diagonals meet at point $O$. Then, $\triangle A O B$ is an isosceles right-angled triangle.
Reasen ( $R$ ): The diagonals of a square are equal and bisect each other at right angles
Reasen ( $R$ ): The diagonals of a square are equal and bisect each other at right angles
- ABoth A and R are true and R is the correct explanation of A
- BBoth A and R are true but R is not the correct explanation of A
- CA is true but R is false
- DA is false but R is true
The sides of a rectangle are in the ratio $5 : 4$ and its perimeter is $90\ cm$. Find its length and breadth.
View full solution →Two adjacent angles of a parallelogram are equal. What is the measure of each of these angles?
In the given figure $ABCD$ is a square. Find the measure of $\angle\text{CAD}.$
View full solution →The lengths of the diagonals of a rhombus are $16\ cm$ and $12\ cm$ respectively. Find the length of each of its sides.
View full solution →In the adjacent figure, $ABCD$ is a rectangle. If $BM$ and $DN$ are perpendiculars from $B$ and $D$ on $AC$, prove that $\triangle\text{BMC}\cong\triangle\text{DNA}.$ Is it true that $BM = DN$?
View full solution →Two adjacent angles of a parallelogram are in the ratio $4 : 5$. Find the measure of each of its angles.
View full solution →$ABCD$ is a parallelogram in which $\angle\text{A}=110^\circ.$ Find the measure of each of the angles $\angle\text{A},\angle\text{B}$ and $\angle\text{D.}$
View full solution →In the adjacent figure, $ABCD$ is a parallelogram and line segments $AE$ and $CF$ bisect the angles $A$ and $C$ respectively. Show that $AE\ ||\ CF$.
View full solution →During a mathematics class, a teacher once gave her students a surprise test to review their knowledge of basic concepts on quadrilaterals. She mentioned the special properties of specific quadrilaterals on different slips and asked each of her students to pick one slip each and identify the quadrilaterals from the given property.
(1) Student A picked the following slip.
A quadrilateral whose all sides, diagonals and angles are equal
A's reply would be
(a) trapezium (b) rhombus (c) rectangle (d) square
(2) Student B picked the following slip.
A quadrilateral whose adjacent sides are equal
B's reply would be
(a) rectangle (b) rhombus (c) trapezium (d) kite
(3) Student C picked the following slip.
A quadrilateral which has the properties of a kite and a parallelogram
C's reply would be
(a) trapezium (b) rhombus (c) rectangle (d) isosceles trapezium
(4) Student D picked the following slip.
A quadrilateral in which only one diagonal bisects the other
D's reply would be
(a) rectangle (b) rhombus (c) trapezium (d) kite
Q.1. Student E picked the following slip.
A quadrilateral in which each diagonals bisects the angles at the vertices through which it passes
E's reply would be
(a) parallelogram (b) rectangle (c) rhombus (d) square
(1) Student A picked the following slip.
A quadrilateral whose all sides, diagonals and angles are equal
A's reply would be
(a) trapezium (b) rhombus (c) rectangle (d) square
(2) Student B picked the following slip.
A quadrilateral whose adjacent sides are equal
B's reply would be
(a) rectangle (b) rhombus (c) trapezium (d) kite
(3) Student C picked the following slip.
A quadrilateral which has the properties of a kite and a parallelogram
C's reply would be
(a) trapezium (b) rhombus (c) rectangle (d) isosceles trapezium
(4) Student D picked the following slip.
A quadrilateral in which only one diagonal bisects the other
D's reply would be
(a) rectangle (b) rhombus (c) trapezium (d) kite
Q.1. Student E picked the following slip.
A quadrilateral in which each diagonals bisects the angles at the vertices through which it passes
E's reply would be
(a) parallelogram (b) rectangle (c) rhombus (d) square
Which of the following statements are true and which are false? The diagonals of a parallelogram are equal.
Name of the following parallelogram.
All the sides are equal and one angle is $90^\circ .$
View full solution →All the sides are equal and one angle is $90^\circ .$
Which of the following statements are true and which are false?
The diagonals of a rectangle are perpendicular to each other.
The diagonals of a rectangle are perpendicular to each other.
Name of the following parallelogram. All the sides are equal and one angle is $60^\circ .$
View full solution →Name of the following parallelogram. The diagonals are equal and the adjacent sides are equal.
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