Write the correct answer in the following: $ABCD$ is a rhombus such that $\angle\text{ACB}=40^\circ.$ then $\angle\text{ADB}$ is:
- A$40^\circ$
- B$45^\circ$
- ✓$50^\circ$
- D$60^\circ$
Answer: C.
View full solution →Question types
Quadrilaterals question types
57 questions across 5 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.
57
Questions
5
Question groups
5
Question types
01
M.C.Q
14 Q→021 Marks Question
5 Q→032 Marks Questions
9 Q→043 Marks Question
3 Q→054 Marks Questions
26 Q→Sample Questions
Quadrilaterals questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
Write the correct answer in the following: A diagonal of a rectangle is inclined to one side of the rectangle at $25^\circ$. The acute angle between the diagonals is:
- A$55^\circ$
- ✓$50^\circ$
- C$40^\circ$
- D$25^\circ$
Answer: B.
View full solution →Write the correct answer in the following:
If bisectors of $\angle \text{A}$ and $\angle \text{B}$ of a quadrilateral $ABCD$ intersect each other at $P$, of $\angle \text{B}$ and $\angle \text{C}$ at $Q$, of $\angle \text{C}$ and $\angle \text{D}$ at $R$ and of $\angle \text{D}$ and $\angle \text{A}$ at S, then $PQRS$ is a:
If bisectors of $\angle \text{A}$ and $\angle \text{B}$ of a quadrilateral $ABCD$ intersect each other at $P$, of $\angle \text{B}$ and $\angle \text{C}$ at $Q$, of $\angle \text{C}$ and $\angle \text{D}$ at $R$ and of $\angle \text{D}$ and $\angle \text{A}$ at S, then $PQRS$ is a:
- ARectangle.
- BRhombus.
- CParallelogram.
- ✓Quadrilateral whose opposite angles are supplementary.
Answer: D.
View full solution →Write the correct answer in the following:
If $APB$ and $CQD$ are two parallel lines, then the bisectors of the angles $APQ, BPQ, CQP$ and $PQD$ form:
If $APB$ and $CQD$ are two parallel lines, then the bisectors of the angles $APQ, BPQ, CQP$ and $PQD$ form:
- AA square.
- BA rhombus.
- ✓A rectangle.
- DAny other parallelogram.
Answer: C.
View full solution →Write the correct answer in the following: The quadrilateral formed by joining the mid-points of the sides of a quadrilateral $PQRS$, taken in order, is a rhombus, if:
- A$PQRS$ is a rhombus.
- B$PQRS$ is a parallelogram.
- CDiagonals of $PQRS$ are perpendicular.
- ✓Diagonals of $PQRS$ are equal.
Answer: D.
View full solution →Can all the four angles of a quadrilateral be obtuse angles? Give reason for your answer.
Diagonals of a parallelogram are perpendicular to each other. Is this statement true? Give reason for your answer.
$D, E$ and $F$ are the mid-points of the sides $BC, CA$ and $AB,$ respectively of an equilateral triangle $ABC.$ Show that $\Delta\text{DEF}$ is also an equilateral triangle.
View full solution →Diagonals of a rectangle are equal and perpendicular. Is this statement true? Give reason for your answer.
Can all the angles of a quadrilateral be right angles? Give reason for your answer.
In quadrilateral $ABCD, \angle\text{A}+\angle\text{D}=180^\circ$ What special name can be given to this quadrilateral?
View full solution →In $\triangle A B C, B C=8 cm$ and $C A=7 cm$. If $D$ and $E$ are respectively the mid-points of $A B$ and $B C$, determine the length of $D E$.
View full solution →$ABCD$ and $AEFG$ are two parallelograms. If $\angle\text{C}=55^\circ,$ determine $\angle\text{F}.$ 
View full solution →Can the angles $110^\circ , 80^\circ , 70^\circ $ and $95^\circ $ be the angles of a quadrilateral? Why or why not?
View full solution →Can all the angles of a quadrilateral be acute angles? Give reason for your answer.
Diagonals $A C$ and $B D$ of a parallelogram $A B C D$ intersect each other at $O$. If $O A=3 cm$ and $O D=2 cm$, determine the lengths of $A C$ and $B D$.
View full solution →$ABCD$ is a trapezium in which $AB \| DC$ and $\angle\text{A}=\angle\text{B}=45^\circ.$ Find angles $C$ and $D$ of the trapezium.
View full solution →All the angles of a quadrilateral are equal. What special name is given to this quadrilateral?
$P$ is the mid-point of the side $CD$ of a parallelogram $ABCD.$ A line through $C$ parallel to $PA$ intersects $AB$ at $Q$ and $DA$ produced at $R.$ Prove that $DA = AR$ and $CQ = Q$
View full solution →A diagonal of a parallelogram bisects one of its angles. Show that it is a rhombus.
$E$ is the mid-point of a median $AD$ of $\Delta\text{ABC}$ and $BE$ is produced to meet $AC$ at $F.$ Show that $\text{AF}=\frac{1}{3}\text{AC}.$
View full solution →$P, Q, R$ and $S$ are respectively the mid-points of sides $AB, BC, CD$ and $DA$ of quadrilateral $ABCD$ in which $AC = BD$ and $\text{AC}\bot\text{BD}.$ Prove that $PQRS$ is a square.
View full solution →Through $A, B$ and $C,$ lines $RQ, PR$ and $QP$ have been drawn, respectively parallel to sides $BC, CA$ and $AB$ of a $\Delta\text{ABC}$ as shown Show that $\text{BC}=\frac{1}{2}QR.$
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