Which of the following is not true for a parallelogram?
- Aopposite sides are equal
- Bopposite angles are equal
- ✓opposite angles are bisected by the diagonals
- Ddiagonal bisects each other
Answer: C.
View full solution →Question types
Quadrilaterals [NEW] question types
198 questions across 8 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.
198
Questions
8
Question groups
5
Question types
01
M.C.Q
99 Q→02Assertion (A) & Reason (B) MCQ
10 Q→03Fill In The Blanks[1 Marks ]
8 Q→04True False[1 Marks ]
8 Q→051 Marks Question
13 Q→062 Marks Questions
8 Q→073 Marks Question
15 Q→084 Marks Questions
37 Q→Sample Questions
Quadrilaterals [NEW] questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
Three angles of a quadrilateral are $75^{\circ}, 90^{\circ}$ and $75^{\circ}$. The fourth angle is
- A$90^{\circ}$
- B$95^{\circ}$
- C$105^{\circ}$
- ✓$120^{\circ}$
Answer: D.
View full solution →The quadrilateral formed by joining the mid-points of the sides of a quadrilateral PQRS. taken in order, is a rhombus, if
- APQRS is a rhombus
- BPQRS is a parallloegram
- Cdiagonals of PQRS are perpendicular
- ✓diagonals of PQRS are equal
Answer: D.
View full solution →The quadrilateral formed by joining the mid-points of the pair of consecutive sides of a quadrilateral PQRS, taken in order, is a rectangle, if
- APQRS is a rectangle
- BPQRS is a parallelogram
- ✓diagonals of PQRS are perpendicular
- Ddiagonals of PQRS are equal
Answer: C.
View full solution →In Fig., D and E are the mid-points of the sides AB and AC respectively of $\triangle A B C$. DE is produced to F. To prove that CF is equal and parallel to DA, we need an additional information which is
- A$\angle D A E=\angle E F C$
- BAE = EF
- ✓DE = EF
- D$\angle ADE=\angle ECF$
Answer: C.
View full solution →Statement-1 (A): The diagonals of a parallelogram bisect each other.
Statement-2 (R): If the diagonals of a parallelogram are equal and intersect at right angle, then it is a square.
Statement-2 (R): If the diagonals of a parallelogram are equal and intersect at right angle, then it is a square.
- ✓Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
- BStatement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
- CStatement-1 is true, Statement-2 is false.
- DStatement-1 is false, Statement-2 is true.
Answer: A.
View full solution →Statement-1 (A): The bisectors of the angles of a parallelogram enclose a rectangle.
Statement-2 (R): In a parallelogram, the bisectors of any two consecutive angles intersect at right angle.
Statement-2 (R): In a parallelogram, the bisectors of any two consecutive angles intersect at right angle.
- ✓Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
- BStatement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
- CStatement-1 is true, Statement-2 is false.
- DStatement-1 is false, Statement-2 is true.
Answer: A.
View full solution →Statement-1 (A): In Fig. if AD is the median of Delta $\triangle A B C$ and E is the mid-point of AD. BE produced meets AC in F, then $A F=\frac{1}{3} A C$.
Statement-2 (R): The line through the mid-point of one side of a triangle, parallel to another side, intersects the third side at its mid-point.
Statement-2 (R): The line through the mid-point of one side of a triangle, parallel to another side, intersects the third side at its mid-point.
- ✓Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
- BStatement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
- CStatement-1 is true, Statement-2 is false.
- DStatement-1 is false, Statement-2 is true.
Answer: A.
View full solution →Statement-1 (A): In a rhombus ABCD, diagonals, AC bisects the angles $\angle A$ as well as $\angle C$.
Statement-2 (R): The diagonals of a rhombus bisect each other at right angle.
Statement-2 (R): The diagonals of a rhombus bisect each other at right angle.
- AStatement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
- ✓Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
- CStatement-1 is true, Statement-2 is false.
- DStatement-1 is false, Statement-2 is true.
Answer: B.
View full solution →Statement-1 (A): If the measures of three angles of a quadrilateral are 130°, 70° and 60°, then the measure of fourth angle is 100°.
Statement-2 (R): The sum of all the angles of a quadrilateral is 360°.
Statement-2 (R): The sum of all the angles of a quadrilateral is 360°.
- ✓Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
- BStatement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
- CStatement-1 is true, Statement-2 is false.
- DStatement-1 is false, Statement-2 is true.
Answer: A.
View full solution →If opposite angles of a quadrilateral are equal, then it is necessarily a ____________ . (parallelogram, rhombus, rectangle)
If one pair of opposite sides are equal and parallel, then the figure is ____________ . (parallelogram, rectangle, trapezium)
If one angle of a parallelogram is a right angle, then it is necessarily a ____________ . (rectangle, square, rhombus)
If in a quadrilateral only one pair of opposite sides are parallel, the quadrilateral is ____________ . (square, rectangle, trapezium)
If consecutive sides of a parallelogram are equal, then it is necessarily a ____________ . (kite, rhombus, square)
Which of the following statements are true (T) and which are false (F)?
In a parallelogram, the diagonals intersect each other at right angles.
In a parallelogram, the diagonals intersect each other at right angles.
Which of the following statements are true (T) and which are false (F)?
In a parallelogram, the diagonals bisect each other.
In a parallelogram, the diagonals bisect each other.
Which of the following statements are true (T) and which are false (F)?
In a parallelogram, the diagonals are equal.
In a parallelogram, the diagonals are equal.
Which of the following statements are true (T) and which are false (F)?
In any quadrilateral, if a pair of opposite sides is equal, it is a parallelogram.
In any quadrilateral, if a pair of opposite sides is equal, it is a parallelogram.
Which of the following statements are true (T) and which are false (F)?
If three sides of a quadrilateral are equal, it is a parallelogram.
If three sides of a quadrilateral are equal, it is a parallelogram.
The perimeter of a parallelogram is 22 cm . If the longer side measures 6.5 cm , what is the measure of shorter side?
In Fig., PQRS is a rhombus in which the diagonal $P R$ is produced to $T$. If $\angle S R T=152^{\circ}$, find $x, y$ and $z$.
View full solution →In Fig, PQRS is an isosceles trapezium. Find x and y.
In Fig., ABCD is a trapezium. Find the values of x and y.
In Fig., ABCD and AEFG are two parallelograms. If $\angle C=58^{\circ}$, find $\angle F$.
View full solution →The sides AB and CD of a parallelogram ABCD are bisected at E and F. prove that EBFD is a parellelogram.
PQRS is a square such that PR and SQ intersect at O. State the measure of $\angle\text{POQ.}$
View full solution →In a parallelogram ABCD, write the sum of angles A and B.
In a parallelogram ABCD, if $\angle\text{D} = 115^\circ,$ then write the measure of $\angle\text{A.}$
View full solution →In a parallelogram ABCD, if $\angle\text{B}=135^\circ,$ determine the measure of its other angles.
View full solution →Three angles of a quadrilateral are respectively equal to 110°, 50° and 40°. Find its fourth angle.
The perimeter of a parallelogram is 22cm.If the longer side measures 6.5cm what is the measure of the shorter side?
The perimeter of a parallelogram is 22cm. If the longer side measures 6.5cm, what is the measure of shorter side?
The angles of a quadrilateral are in the ratio 3 : 5 : 9 : 13. Find all the angles of the quadrilateral.
In a triangle $\angle\text{ABC},$ $\angle\text{A}=50^\circ,$ $\angle\text{B}=60^\circ$ andFind the measures of the angles of the triangle formed by joining the mid-points of the sides of this triangle.
View full solution →Two opposite angles of a parallelogram are (3x - 2)° and (50 - x)°. Find the measure of each angle of the parallelogram.
The diagonals of a rectangle ABCD meet at O, If $\angle\text{BOC}=44^\circ,$ find $\angle\text{OAD}.$
View full solution →Show that, the line segments joining the mid-points of opposite sides of a quadrilateral bisects each other.
P and Q are the point of trisection of the diagonal BD of a parallelogram ABCD. prove that CQ is parallel to AP. prove also that AC bisects PQ.
Let ABC be an isosceles triangle in which AB = AC. If D, E, F be the mid points of the, sides BC, CA and AB respectively, show that the segment AD and EF bisect each other at right angles.
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