If opposite angles of a rhombus are (2x)° and (3x – 40)°, then the value of x is ____.
- A100°
- B80°
- C160°
- ✓40°
Answer: D.
View full solution →Question types
Quadrilaterals question types
61 questions across 8 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.
61
Questions
8
Question groups
5
Question types
01
MCQ(1M)
3 Q→02True False With Reason
6 Q→031 Mark Question
3 Q→042 Mark Question
10 Q→053 Mark Question
14 Q→064 Mark Question
17 Q→075 Mark Question
7 Q→08Activity Based Questions.
1 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.
If the diagonal of a square is $22\sqrt2$ cm, then the perimeter of square is ____.
- A$24 cm$
- B$24\sqrt2 cm$
- ✓$48 cm$
- D$48\sqrt2 cm$
Answer: C.
View full solution →If all pairs of adjacent sides of a quadrilateral are congruent, then it is called ____.
- Arectangle
- Bparallelogram
- Ctrapezium
- ✓rhombus
Answer: D.
View full solution →Every parallelogram is a rectangle.
Every square is a rhombus.
Every square is a rectangle,
Every rectangle is a parallelogram.
Every rhombus is a rectangle,
Points $E$ and $F$ are mid points of seg $A B$ and seg $A C$ of $\triangle A B C$ respectively. If $\mathrm{EF}=5.6$ then find the length of $\mathrm{BC}$.
View full solution →Prove the Theorem : Diagonals of a rectangle are congruent.
Prove that every rhombus is a parallelogram.
To verify the different properties of quadrilaterals.
Draw a parallelogram PQRS. Draw diagonals PR and QS. Denote the intersection of diagonals by letter O. Compare the two parts of each diagonal with a divider. What do you find?
Draw five parallelograms by taking various measures of lengths and angles.
Prove the Theorem : A quadrilateral is a parallelogram if a pair of its opposite sides is parallel and congruent.
$\mathrm{ABCD}$ is a parallelogram. If $\angle \mathrm{A}=(4 x+13)^{\circ}$ and $\angle \mathrm{D}=(5 x-22)^{\circ}$ then find the measures of $\angle \mathrm{B}$ and $\angle \mathrm{C}$.
View full solution →Prove that the quadrilateral formed by joining the midpoints of sides of a quadrilateral in order is a parallelogram.
In $\square \mathrm{PQRS}$, side $\mathrm{PS} \|$ side $\mathrm{QR}$ and side $\mathrm{PQ} \cong$ side $\mathrm{SR}$, side $\mathrm{QR}>$ side $\mathrm{PS}$ then prove that $\angle \mathrm{PQR} \cong \angle \mathrm{SRQ}$
View full solution →Measures of angles of $\square \mathrm{ABCD}$ are in the ratio $4: 5: 7: 8$. Show that $\square \mathrm{ABCD}$ is a trapezium.
View full solution →Prove the Theorem : Diagonals of a rhombus are perpendicular bisectors of each other.
$\square \mathrm{PQRS}$ is parallelogram. $\mathrm{M}$ is the midpoint of side $\mathrm{PQ}$ and $\mathrm{N}$ is the mid point of side RS. Prove that $\square$ PMNS and $\square$ MQRN are parallelograms.
View full solution →Diagonals of a rectangle PQRS are intersecting in point M. If ∠QMR = 50°, then find the measure of ∠MPS.
Diagonals $PR$ and $QS$ of a rhombus $\text PQRS$ are $20\ cm$ and $48\ cm$ respectively. Find the length of side $PQ$.
View full solution →Ratio of two adjacent sides of a parallelogram is 3 : 4, and its perimeter is 112 cm. Find the length of its each side.
If diagonal of a square is $13\ cm$, then find its side.
View full solution →Adjacent sides of a rectangle are $7\ cm$ and $24\ cm$. Find the length of its diagonal.
View full solution →In the adjoining figure, □ABCD is a trapezium. AB || DC. Points M and N are midpoints of diagonals AC and DB respectively, then prove that MN || AB.
In the adjoining figure, $\square A B C D$ is a trapezium. $A B \| D C$. Points $P$ and $Q$ are midpoints of seg $A D$ and seg $B C$ respectively. Then prove that $P Q \| A B$ and $P Q=\frac{1}{2}(A B+D C)$.
View full solution →
In the adjoining figure, if seg AB || seg PQ , seg AB ≅ seg PQ, seg AC || seg PR, seg AC ≅ seg PR, then prove that seg BC || seg QR and seg BC ≅ seg QR.
In □ABCD, side BC < side AD, side BC || side AD and if side BA ≅ side CD, then prove that ∠ABC = ∠DCB.
Given: side BC < side AD, side BC || side AD, side BA = side CD
To prove: ∠ABC ≅ ∠DCB
Construction: Draw seg BP ⊥ side AD, A – P – D
seg CQ ⊥ side AD, A – Q – D
In □ABCD, side BC || side AD, side AB ≅ side DC. If ∠A = 72°, then find the measures of ∠B and ∠D.
Construction: Draw seg BP ⊥ side AD, A – P – D, seg CQ ⊥ side AD, A – Q – D.
Construction: Draw seg BP ⊥ side AD, A – P – D, seg CQ ⊥ side AD, A – Q – D.
Prove the Theorem : If both the pairs of opposite angles of a quadrilateral are congruent then it is a parallelogram.
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