Construct a quadrilateral XYZT in which XY = XZ = 5.7 cm YZ = 4.5 cm ZX = 4.6 cm and XT = 5 cm.
Question types
Quadrilaterals question types
143 questions across 5 question groups — pick any mix to generate a MATHEMATICS paper with step-by-step answer keys.
143
Questions
5
Question groups
5
Question types
01
[2 Mark Question Answer]
39 Q→02[3 marks sum]
28 Q→03[4 marks sum]
15 Q→04[5 marks sum]
11 Q→05MCQ
50 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.
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Construct a quadrilateral ABCD in which AB = AD = 5.3 cm , BC CD = 5 cm and diagonal BD = 6.4 cm.
Construct a quadrilateral PQRS in which $PQ =4.5 cm, QR =5.6 cm, RS =4.1 cm$, $\angle Q =60$ and $\angle R =120$.
View full solution →Construct a quadrilateral UVWZ in which UV $=6 cm, VW =5.3 cm, UZ =5 cm$, $\angle U =60$ and $\angle V =75$.
View full solution →Construct a quadrilateral ABCD in which $AB = CD =5.1 cm, BC =4.7 cm$, $DA =4.2 cm$ and $\angle BCD =60$.
View full solution →Construct a parallelogram PQRS in which $QR =4.7 cm, \angle Q =120$ and $PQ =2.8 cm$.
View full solution →Construct a parallelogram ABCD in which $BC =6 cm, CD =4 cm$ and $\angle C =60$.
View full solution →Construct a parallelogram ABCD in which AB = 4.8cm BC = 3.5 cm and diagonal AC = 5.4 cm.
Construct a parallelogram ABCD in which BC = 5 cm CD = 3 cm and diagonal BD = 6 cm.
In the given figure, ABCD is a kite whose diagonals intersect at O . If $\angle DAB =54$ and $\angle BCD =76$, calculate :
(i) $\angle ODA$
(ii) $\angle OBC$.
View full solution →(i) $\angle ODA$
(ii) $\angle OBC$.
In the given figure, ABCD is a parallelogram. Side DC is produced to E and $\angle BCE =105$.
Calculate $\angle A , \angle B , \angle C$ and $\angle D$.
View full solution →Calculate $\angle A , \angle B , \angle C$ and $\angle D$.
DEC is an equilateral triangle in a square ABCD . If BD and CE intersect at O and $\angle COD =x$, find the value of $x$.
View full solution →Which of the following quadrilaterals can you construct if you know the length of two its diagonals?
Parallelogram$\quad$Rectangle$\quad$Rhombus$\quad$Square
View full solution →Parallelogram$\quad$Rectangle$\quad$Rhombus$\quad$Square
In the given figure, ABCD is a rhombus in which $\angle A =72^{\circ}$. If $\angle CBD =x^{\circ}$, find the value of $x$.
View full solution →In the adjoining figure, equilateral $\triangle E D C$ surmounts square ABCD . If $\angle DEB =x^{\circ}$, find the value of $x$.
View full solution →Show that the bisectors of the angles of a parallelogram enclose a rectangle.
In the given figure, ABCD is a parallelogram and X, Y are points on diagonal BD such that DX = BY Prove that CXAY is a parallelogram.
In the adjoining figure, ABCD is a parallelogram.
Line segments AX and CY bisect $\angle A$ and $\angle C$ respectively.
Prove that :
(i) $\triangle ADX \cong \triangle CBY$
(ii) $AX = CY$
(iii) $AX \| CY$
(iv) AYCX is a parallelogram.
View full solution →Line segments AX and CY bisect $\angle A$ and $\angle C$ respectively.
Prove that :
(i) $\triangle ADX \cong \triangle CBY$
(ii) $AX = CY$
(iii) $AX \| CY$
(iv) AYCX is a parallelogram.
In the given figure, ABCD is a rhombus and $\triangle EDC$ is equilateral.
If $\angle BAD =78$, calculate :
(i) $\angle CBE$
(ii) $\angle DBE$.
View full solution →If $\angle BAD =78$, calculate :
(i) $\angle CBE$
(ii) $\angle DBE$.
In the given figure, ABCD is an isosceles trapezium in which $\angle CDA =2 x$ and $\angle BAD =3 x$.
Find all the angles of the trapezium.
View full solution →Find all the angles of the trapezium.
The diagonals of a quadrilateral intersect at right angles and it has exactly one axis of symmetry. The quadrilateral is a:
- Asquare
- Brhombus
- ✓kite
- Dnone of these
Answer: C.
View full solution →ABCD is a trapezium and P and Q are the mid-points of the diagonals of AC and BD . Then PQ is equal to:
- A$\frac{1}{2} AB$
- B$\frac{1}{2} CD$
- ✓$\frac{1}{2}( AB - CD )$
- D$\frac{1}{2}( AB + CD )$
Answer: C.
View full solution →Diagonals of a quadrilateral ABCD bisect each other. If $\angle A =35^{\circ}$, then $\angle B$ is equal to:
- ✓$145^{\circ}$
- B$135^{\circ}$
- C$155^{\circ}$
- D$35^{\circ}$
Answer: A.
View full solution →If bisectors of $\angle A$ and $\angle B$ of a parallelogram ABCD intersect each other at P , of $\angle B$ and $\angle C$ at Q , of $\angle C$ and $\angle D$ at R and of $\angle D$ and $\angle A$ at S , then PQRS is a:
- ✓rectangle
- Brhombus
- Cparallelogram
- Dquadrilateral whose opposite angles are supplementary.
Answer: A.
View full solution →Assertion (A): Every square is a parallelogram.
Reason (R): In a square as well as in a parallelogram, the diagonals two diagonals are equal in length.
Reason (R): In a square as well as in a parallelogram, the diagonals two diagonals are equal in length.
- ✓A is true, R is false
- BA is false, R is true
- CBoth A and R are true
- DBoth A and R are false.
Answer: A.
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