The diagonals of a rectangle are $2 x+1$ and $3 x-1$, respectively. Find the value of $x$.
- A1
- ✓2
- C3
- D4
Answer: B.
View full solution →Question types
Understanding Quadrilaterals question types
112 questions across 11 question groups — pick any mix to generate a MATHS paper with step-by-step answer keys.
112
Questions
11
Question groups
5
Question types
01
M.C.Q. [1 Marks Each]
15 Q→02TRUE-FLASE [1 Marks Each]
13 Q→03Assertion (A) & Reason (B) MCQ
3 Q→042 Marks Questions
23 Q→053 Marks Question
21 Q→065 Marks Questions
2 Q→07Case study (4 Marks)
1 Q→08MATCH THE FOLLOWING.
2 Q→091 Marks Question
9 Q→10BLANKS [1 Marks Each]
5 Q→114 Mark Question
18 Q→Sample Questions
Understanding Quadrilaterals questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
Vanita folds a rectangular sheet. The folded sheet is shown below.
What is the length of the sheet?
What is the length of the sheet?
- A8 cm
- B$\sqrt{10} cm$
- ✓10 cm
- D12 cm
Answer: C.
View full solution →Prisha has a farm land which is triangular shape.
What is the sum of all the exterior angles taken in an order of the farm land?
What is the sum of all the exterior angles taken in an order of the farm land?
- A$90^{\circ}$
- B$180^{\circ}$
- ✓$360^{\circ}$
- DCannot be determined
Answer: C.
View full solution →The perimeter of a parallelogram whose parallel sides have length equal to 12 cm and 7 cm is
- A21 cm
- B42 cm
- C19 cm
- ✓38 cm
Answer: D.
View full solution →Which of the following quadrilaterals has two pairs of adjacent sides equal and its diagonals intersect at $90^{\circ}$ ?
- ASquare
- ✓Kite
- CRhombus
- DRectangle
Answer: B.
View full solution →All squares are frapeziums.
All parallelograms are trapeziums.
All rhombuses are kites.
All kites are rhombuses.
All squares are not parallelograms.
Assertion (A) A square is both a rectangle and a rhombus.
Reason (R) A square has all sides equal, and its opposite sides are parallel.
Reason (R) A square has all sides equal, and its opposite sides are parallel.
- ✓Both 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.
Answer: A.
View full solution →Assertion (A) A kite is not a convex quadrilateral.
Reason (R) A quadrilateral has 2 diagonals.
Reason (R) A quadrilateral has 2 diagonals.
- 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.
- ✓A is false but R is true.
Answer: D.
View full solution →Assertion (A) In a trapezium, the non-parallel sides are equal in length.
Reason (R) Trapezium have one pair of opposite sides that are parallel.
Reason (R) Trapezium have one pair of opposite sides that are parallel.
- 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.
- ✓A is false but R is true.
Answer: D.
View full solution →Take a cut-out of a parallelogram, say $A B C D$ in adjoining figure. Let its diagonals $\overline{A C}$ and $\overline{D B}$ meet at O.
Find the mid-point of $\overline{A C}$ by a fold, placing $C$ on $A$. Is the mid-point same as O?
Does this show that diagonal $\overline{D B}$ bisects the diagonal $\overline{A C}$ at the point $O$ ? Discuss it with your friends.
Repeat the activity to find, where the mid-point of $\overline{D B}$ could lie.
View full solution →Find the mid-point of $\overline{A C}$ by a fold, placing $C$ on $A$. Is the mid-point same as O?
Does this show that diagonal $\overline{D B}$ bisects the diagonal $\overline{A C}$ at the point $O$ ? Discuss it with your friends.
Repeat the activity to find, where the mid-point of $\overline{D B}$ could lie.
Take two identical $30^{\circ}-60^{\circ}-90^{\circ}$ set squares and form a parallelogram as before. Does the following figure obtained help you to confirm the above property?
View full solution →Take two identical set squares with angles $30^{\circ}-60^{\circ}-90^{\circ}$ and place them adjacently to form a parallelogram as shown in the following figure. Does this help you to verify the above property?
View full solution →Take four set-squares from your and your friend's Instrument boxes. Use different numbers of them to place side-by-side and obtain different trapeziums.
If the non-parallel sides of a trapezium are of equal length, we call it an Isosceles trapezium. Did you get an isosceles trapezium in any of your Investigations given above?
If the non-parallel sides of a trapezium are of equal length, we call it an Isosceles trapezium. Did you get an isosceles trapezium in any of your Investigations given above?
Can a trapezium have all angles equal? Can it have all sides equal? Explain.
After showing $\text{m} \angle \text{R = m} \angle \text{N}=70^{\circ},$ can you find $\text{m} \angle \text{I}$ and $\text{m} \angle \text{G}$ by any other method?
View full solution →Find $x$, in the following figures.
View full solution →.Find the value of $\angle P$ and $\angle S$ if $\overline{S P} \| \overline{R Q}$ In the following figure. If you find $m \angle R$, Is there more than one method to find $m \angle P$?
View full solution →The adjacent figure HOPE is a parallelogram. Find the angle $x, y$ and $z$. State the properties you use to find them.
View full solution →The measures of two adjacent angles of a parallelogram are in the ratio $3: 2$. Find each angle of the parallelogram.
View full solution →Consider the following parallelograms. Find the values of the unknowns $x, y$ and $z$
View full solution →Given here are some figures.
Classify each of them on the basis of the following
(a) Simple curve$\quad$(b) Simple closed curve
(c) Polygon $\qquad\text{ }$ (d) Convex polygon
(e) Concave polygon
View full solution →Classify each of them on the basis of the following
(a) Simple curve$\quad$(b) Simple closed curve
(c) Polygon $\qquad\text{ }$ (d) Convex polygon
(e) Concave polygon
A rectangular MORE is shown below :
Answer the following questions by giving appropriate reason.
(i) Is $R E=O M?$
(ii) Is $\angle MYO =\angle R X E?$
(iii) Is $\angle M O Y=\angle R E X?$
(iv) Is $\triangle M Y O \cong \triangle R X E?$
View full solution →Answer the following questions by giving appropriate reason.
(i) Is $R E=O M?$
(ii) Is $\angle MYO =\angle R X E?$
(iii) Is $\angle M O Y=\angle R E X?$
(iv) Is $\triangle M Y O \cong \triangle R X E?$
View full solution →
| Column A (Information about a quadrilateral ABCD) | Column B (Type of Quadrilateral) |
| (a) If AB = AD and BC = CD | (i) Square |
| (b) If $AB\|CD$ and AD = BC | (ii) Kite |
| (c) If $AB\|CD$ and $BC\|AD$ | (iii) Isosceles trapezium |
| (d) If AC = BD and ABCD is a parallelogram | (iv) Parallelogram |
| (v) Rectangle |
Find the measure of exterior angle of a regular pentagon and an exterior angle of a regular decagon. What is the ratio between these two angles?
Each interior angle of a polygon is $108^{\circ}.$ Find the number of sides of the polygon.
View full solution →In the following figure, find the value of x.
Find the value of x in the trapezium ABCD given below.
If four angles of a quadrilateral are in the ratio 3: 8: 10: 3, then find its all angles.
The adjacent angles of a parallelogram are _____________.
_____________ is a regular quadrilateral.
If the diagonals of a quadrilateral bisect each other, it is a _____________.
If PQRS is a parallelogram, then $\angle \text{Q}-\angle \text{S}$ is equal to _____________.
View full solution →A regular polygon is a polygon whose all sides are equal and all _____________ are equal.
Take identical cut-outs of congruent triangles of sides 3 cm, 4 cm and 5 cm . Arrange them as shown in the figure.
You get a trapezium (check it!) which are the parallel sides here? Should the non-parallel sides be equal? You can get two more trapeziums using the same set of triangles. Find out them and discuss their shapes.
You get a trapezium (check it!) which are the parallel sides here? Should the non-parallel sides be equal? You can get two more trapeziums using the same set of triangles. Find out them and discuss their shapes.
Take a regular hexagon, in the given figure.
(i) What is the sum of the measures of its exterior angles $x, y, z, p, q$ and $r$ ?
(ii) Is $x=y=z=p=q=r$ ? Why?
(iii) What is the measure of each?
(a) Exterior angle$\qquad$$\quad$ (b) Interior angle
(iv) Repeat this activity for the cases of
(a) A regular octagon $\quad$ (b) A regular 20-gon
View full solution →(i) What is the sum of the measures of its exterior angles $x, y, z, p, q$ and $r$ ?
(ii) Is $x=y=z=p=q=r$ ? Why?
(iii) What is the measure of each?
(a) Exterior angle$\qquad$$\quad$ (b) Interior angle
(iv) Repeat this activity for the cases of
(a) A regular octagon $\quad$ (b) A regular 20-gon
In the above figure, both RISK and CLUE are parallelograms, find the value of $x$.
The following figures GUNS and RUNS are parallelograms. Find $x$ and $y$. (lengths are in cm)
View full solution →Given a parallelogram ABCD Complete each statement along with the definition or property used.
(i) $A D=$ _____________ $\qquad\text{ }$ (ii) $\angle D C B=$ _____________
(iii) $O C=$ _____________$\qquad$ (iv) $m \angle D A B+m \angle C D A=$ _____________
View full solution →(i) $A D=$ _____________ $\qquad\text{ }$ (ii) $\angle D C B=$ _____________
(iii) $O C=$ _____________$\qquad$ (iv) $m \angle D A B+m \angle C D A=$ _____________
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