Teachers can assign these Ganita Prakash Class 8 Worksheet and Class 8 Maths Chapter 4 Understanding Quadrilaterals Worksheet with Answers Pdf Download for daily practice.
Class 8 Maths Chapter 4 Understanding Quadrilaterals Worksheet with Answers Pdf
Understanding Quadrilaterals Class 8 Maths Worksheet
Class 8 Maths Chapter 4 Worksheet with Answers – Class 8 Understanding Quadrilaterals Worksheet
Multiple Choice Questions.
Question 1.
A trapezium in which non-parallel sides are equal, is called
(a) a right trapezium
(b) an equilateral trapezium
(c) an isosceles trapezium
(d) None of these
Answer:
(c) an isosceles trapezium
Question 2.
If a quadrilateral has exactly two pairs of equal adjacent sides, then it is called
(a) parallelogram
(b) square
(c) rectangle
(d) kite
Answer:
(d) kite
Question 3.
Which of the following is a property of a parallelogram?
(a) The diagonals bisect each other at right angles
(b) The diagonals are perpendicular to each other
(c) All the angles are equal
(d) Opposite sides are parallel
Answer:
(d) Opposite sides are parallel
Question 4.
If a pair of opposite sides of a quadrilateral are equal and parallel, then it is a
(a) parallelogram
(b) kite
(c) trapezium
(d) None of these
Answer:
(a) parallelogram
Question 5.
Which of the following can be four interior angles of a parallelogram?
(a) 140°, 20°, 40°, 160°
(b) 160°, 20°, 20°, 160°
(c) 150°, 30°, 90°, 60°
(d) 100°, 80°, 90°, 90°
Answer:
(b) 160°, 20°, 20°, 160°
Question 6.
In which of the following quadrilateral the diagonals bisects each other at right angles?
(a) Rectangle
(b) Square
(c) Parallelogram
(d) Trapezium
Answer:
(b) Square
Question 7.
A quadrilateral whose opposite sides are parallel and equal and all angles are right angles is
(a) Rhombus
(b) Parallelogram
(c) Rectangle
(d) Kite
Answer:
(c) Rectangle
Question 8.
In a parallelogram ABCD, if ∠B = 70° then, ∠D is equal to
(a) 110°
(b) 20°
(c) 30°
(d) 70°
Answer:
(d) 70°
Question 9.
In a kite, which of the following is always true?
(a) All sides are equal
(b) Opposite angles are equal
(c) One diagonal bisects the other at right angles
(d) All angles are 90°
Answer:
(c) One diagonal bisects the other at right angles
Question 10.
If a parallelogram has diagonals equal and perpendicular, it must be a
(a) rectangle
(b) rhombus
(c) square
(d) kite
Answer:
(c) square
Question 11.
Which of the following is not necessarily true for a rhombus?
(a) Diagonals are equal
(b) Opposite angle are equal
(c) Opposite sides are parallel
(d) Diagonals bisects each other at right angles
Answer:
(a) Diagonals are equal
Question 12.
Which quadrilateral can be both a kite and a parallelogram?
(a) Square
(b) Rectangle
(c) Rhombus
(d) Trapezium
Answer:
(c) Rhombus
Question 13.
Which of the following quadrilateral has diagonals that are equal but not perpendicular?
(a) Kite
(b) Rectangle
(c) Rhombus
(d) Trapezium
Answer:
(b) Rectangle
Question 14.
Which of the following statements is false.
(a) Every square is a rectangle.
(b) Every rhombus is a parallelogram.
(c) Every Trapezium is a parallelogram.
(d) Every square is a rhombus.
Answer:
(c) Every Trapezium is a parallelogram.
Question 15.
If a quadrilateral has three right angles, the fourth angle must be
(a) 60°
(b) 90°
(c) 120°
(d) Can not determined
Answer:
(b) 90°
Question 16.
One of the diagonals of a rhombus is equal to a side of the rhombus. The angles of the rhombus are
(a) 60°, 80°
(b) 60°, 120°
(c) 120°, 240°
(d) 100°, 120°
Answer:
(b) 60°, 120°
Question 17.
ABCD is a rhombus. If ∠ACB = 40°, then ∠ADB is equal to
(a) 40°
(b) 45°
(c) 50°
(d) 60°
Answer:
(c) 50°
Question 18.
The diagonals of a parallelogram ABCD intersect at O. If ∠BOC = 90° and ∠BDC – 50° then ∠OAB is equal to
(a) 10°
(b) 40
(c) 50°
(d) 90°
Answer:
(b) 40
Question 19.
If two adjacent angles of a parallelogram are (5x – 5)° and (10x + 35)° then the ratio of these angles is
(a) 1 : 3
(b) 2 : 3
(C) 1 : 4
(d) 1 : 2
Answer:
(a) 1 : 3
Question 20.
The angles of a quadrilateral are in the ratio 1 : 2 : 3 : 4. The smallest angle is
(a) 72°
(b) 144°
(c) 36°
(d) 18°
Answer:
(c) 36°
Question 21.
In the given figure, if ABC and DBF are two straight lines, then the value of x is
(a) 60°
(b) 70°
(c) 80°
(d) 85°
Answer:
(b) 70°
Question 22.
In the given figure, if ABCD is a rhombus, then the value of (x – y) is
(a) 50°
(b) 40°
(c) 30°
(d) 20°
Answer:
(b) 40°
Question 23.
In a square ABCD, if the diagonals bisect at O. Then, A AOB is
(a) an equilateral triangle
(b) an isosceles but not a right angled triangle
(c) a right angled but not an isosceles triangle
(d) an isosceles right angled triangle
Answer:
(d) an isosceles right angled triangle
Question 24.
For which of the following quadrilaterals, diagonals are perpendicular to each other?
(a) parallelogram
(b) trapezium
(c) kite
(d) rectangle C
Answer:
(c) kite
Assertion And Reason-Based Questions.
1. Assertion (A) A diagonal and side of a rhombus are of equal length then the measure of angles of the rhombus are 60°, 120°, 60° and 120°.
Reason (R) All rhombus are parallelograms.
(a) Both assertion and reason are true and reason is the correct explanation for assertion.
(b) Both assertion and reason are true but reason is not the correct explanation for assertion.
(c) Assertion is true and reason is false.
(d) Assertion is false and reason is true.
Answer:
(b) Both assertion and reason are true but reason is not the correct explanation for assertion.
2. Assertion (A) Sum of all interior angles of a quadrilateral is 360°.
Reason (R) A parallelogram with one angle 90° is a rectangle.
(a) Both assertion and reason are true and reason is the correct explanation for assertion.
(b) Both assertion and reason are true but reason is not the correct explanation for assertion.
(c) Assertion is true and reason is false.
(d) Assertion is false and reason is true.
Answer:
(b) Both assertion and reason are true but reason is not the correct explanation for assertion.
3. Assertion (A) The value of x in the given parallelogram is 115°.
Reason (R) The opposite angles of a parallelogram are equal.
(a) Both assertion and reason are true and reason is the correct explanation for assertion.
(b) Both assertion and reason are true but reason is not the correct explanation for assertion.
(c) Assertion is true and reason is false.
(d) Assertion is false and reason is true.
Answer:
(a) Both assertion and reason are true and reason is the correct explanation for assertion.
4. Assertion (A) The value of x in the given trapezium PQRS is 135°.
Reason (R) Trapezium is a quadrilateral with one pair of parallel sides.
(a) Both Assertion and Reason are true and Reason is the correct explanation for Assertion.
(b) Both Assertion and Reason are true but Reason is not the correct explanation for Assertion.
(c) Assertion is true and Reason is false.
(d) Assertion is false and Reason is true.
Answer:
(d) Assertion is false and Reason is true.
Fill in the blanks.
1. In isoscales trapezium, the non-parallel sides are of ________ length.
Answer:
equal
2. ________ is a quadrilateral with one pair of parallel sides.
Answer:
trapezium
3. ________ is a quadrilateral which has two pairs of equal consecutive sides.
Answer:
rhombus
4. If the diagonals of quadrilateral bisect each other, then it is a ________.
Answer:
parallelogram
5. In a parallelogram ABCD, AB|| ________ and ________ || AD.
Answer:
CD. BC
6. In a parallelogram ABCD, if ∠A = 120°, then ∠C is equal to ________.
Answer:
120°
7. The sum of adjacent angles in a parallelogram are ________.
Answer:
180°
8. A rhombus has all the properties of a and also that of a ________.
Answer:
parallelogram, kite
9. The diagonals of a rhombus are ________ of one another.
Answer:
perpendicular bisectors
10. In a rectangle, the diagonals are ________ in length and each other.
Answer:
equal, bisect
11. A quadrilateral whose all the sides are equal, opposite angles are equal and the diagonals bisect each other at right angles is a ________.
Answer:
square
12. A quadrilateral has three acute angles. If each measure is 80° then the measure of fourth angle is ________.
Answer:
120°
13. The ________ of a rhombus are bisectors of one another.
Answer:
diagonals
14. The measure of ________ angle of concave quadrilateral is more than 180°.
Answer:
one interior
15. In trapezium ABCD with AS || CD if ∠A = 100° then ∠D = ________.
Answer:
80°
State whether the statements given below are true or false.
1. The consecutive angles of a quadrilateral are always supplementary.
Answer:
False
2. In a trapezium, opposite angles are equal.
Answer:
False
3. In a trapezium, opposite sides are equal.
Answer:
False
4. In a kite, diagonals are perpendicular to one another.
Answer:
True
5. In a kite, one pair of opposite angles are equal.
Answer:
True
6. The angles of a quadrilateral are in the ratio 1:2 :3 : 4. Then, the smallest angle is 30°
Answer:
False
7. The diagonals of a rectangle ABCD intersect at O. If ∠BOC = 600, then ∠ODA is 56°.
Answer:
False
8. In the given figure, if PQRS is a rhombus with ∠PQR = 56° then ∠PRS is 62°.
Answer:
True
9. In the given figure, if ∠P and ∠R are in the ratio 3 :7, then the value of a is 120°.
Answer:
False
Match The Columns.
Question 1.
If ABCD is a parallelogram then match the following.
| Column I | Column II |
| (i) AB and DC are | (a) opposite angles |
| (ii) ∠B and ∠D are | (b) adjacent angles |
| (iii) AB and BC are | (c) diagonals |
| (iv) AC and BD are | (d) opposite sides |
| (v) ∠C and ∠D are | (e) adjacent sides |
Answer:
| Column I | Column II |
| (i) AB and DC are | (d) opposite sides |
| (ii) ∠B and ∠D are | (a) opposite angles |
| (iii) AB and BC are | (e) adjacent sides |
| (iv) AC and BD are | (c) diagonals |
| (v) ∠C and ∠D are | (b) adjacent angles |
Question 2.
| Column I | Column II |
| (i) A quadrilateral, which has one pair of parallel sides is called | (a) Kite |
| (ii) A quadrilateral whose 2 pairs of adjacent sides and only two angles are equal is called | (b) Square |
| (iii) A quadrilateral whose opposite sides are equal and parallel is called | (c) Trapezium |
| (iv) A quadrilateral whose all sides are of equal length and its diagonals are generally not equal is called | (d) Parallelogram |
| (v) A quadrilateral whose all sides are of equal length and diagonals are also equal is called | (e) Rhombus |
Answer:
| Column I | Column II |
| (i) A quadrilateral, which has one pair of parallel sides is called | (c) Trapezium |
| (ii) A quadrilateral whose 2 pairs of adjacent sides and only two angles are equal is called | (a) Kite |
| (iii) A quadrilateral whose opposite sides are equal and parallel is called | (d) Parallelogram |
| (iv) A quadrilateral whose all sides are of equal length and its diagonals are generally not equal is called | (e) Rhombus |
| (v) A quadrilateral whose all sides are of equal length and diagonals are also equal is called | (b) Square |
Question 3.
Answer:
(i) → (b)
(ii) → (C)
(iii) → (a)
(iv) → (d)
Complete the table. (One has been done for you).
Question 1.
Answer:
(i) and (ii) opposite sides are parallel and equal and opposite angles are equal.
(iii) Square, all the sides and diagonals are equal. All angles are 90°.
(iv) Opposite sides and diagonals are equal.
Question 2.
| Statements | Always | Sometimes | Never |
| (i) Rhombuses are squares | ✓ | ||
| (ii) Trapeziums are quadrilaterals | |||
| (iii) Squares are rhombuses | |||
| (iv) Trapeziums are parallelograms | |||
| (v) Parallelograms are quadrilaterals | |||
| (vi) Parallelograms are rectangle |
Answer:
(ii) Always
(iii) Always
(iv) Never
(v) Always
(vi) Sometimes
Question 3.
Observe the following parallelograms and put the values of unknown a, b, c in the given table.
Answer:
(i) 100°, 80°
(ii) 130°, 130 i°, 130°
(iii) 80°, 80°, 260°
(iv) 28°, 112°, 168°
Very Short Answer Type Questions.
Question 1.
Three angles of a quadrilateral are equal. Fourth angle is of measure 150°. What is the measure of equal angles.
Answer:
70°
Question 2.
Two opposite angles of a parallelogram are (3x – 2)° and (50 – x)°. Find the measure of each angle of the parallelogram.
Answer:
37°, 143°
Question 3.
Two adjacent angles of a parallelogram are equal. What is the measure of each?
Answer:
90°
Question 4.
In the following figure, RENT is a rectangle. Its diagonals meet at 0. Find x, if OR = 3x + 7 and OT = 4x + 2
Answer:
5
Question 5.
Construct a square whose diagonal is 4 cm.
Answer:
Do yourself
Question 6.
What is the sum of all interior angles of quadrilateral?
Answer:
360°
Question 7.
If four angles of a quadrilateral are in the ratio of 1 : 2 : 4 : 5. Find the angles,
Answer:
30°, 60°, 120°, 150°
Question 8.
In a quadrilateral, if two angles are in the ratio 1:2. Find these angles.
Answer:
60°, 120°
Question 9.
If three angles of a quadrilateral are 49°, 70° and 121°. Find the fourth angle.
Answer:
120°
Question 10.
In a parallelogram, if one angle is 90° then find the other three angles.
Answer:
90°, 90°, 90°
Question 11.
In the given figure ABCD is a parallelogram, find ZD.
Answer:
130°
Question 12.
In the given figure, find the value of x.
Answer:
20°
Question 13.
Find x + y in the given figure if PQRS is a parallelogram.
Answer:
74°
Question 14.
In the given parallelogram, find ∠ADC if ∠4DB = ∠BDC
Answer:
110°
Question 15.
Find x + y in the given parallelogram MNOP.
Answer:
105°
Short Answer Type Questions.
Question 1.
In the given kite WEAR, ∠WEA = 70° and ∠ARW = 80°. Find the remaining two angles.
Answer:
105°, 105°
Question 2.
In the given figure, if HOPE is a rhombus, then find ∠PEO and ∠POE.
Answer:
60°, 60°
Question 3.
In the given figure, PQRS is a trapezium in SP || RQ, then find the measures of ∠P and ∠R.
Answer:
50°, 90°
Question 4.
The diagonals of a rhombus ABCD intersect at 0. If AC = 8 cm and J3D = 6 cm. Find the length of its sides.
Answer:
5 cm
Question 5.
In a rectangle PQRS, ∠OPQ = 38°. Find ∠RSQ, where O is the intersection point of diagonals.
Answer:
52°
Question 6.
In a square ABCD, AB = (5a – 17) cm and BC = (2a + 4) cm. Find the length of AD.
Answer:
18 cm
Question 7.
In the given figure, ABCD is a parallelogram. Find the values of x, y and z.
Answer:
80°, 70°, 30°
Question 8.
In a trapezium KLMN, ∠M + ∠L = 180°. What will be the sum of ∠N + ∠K? Also, which of its two sides are parallel?
Answer:
180°, KL ML
Question 9.
In the given figure, ABCD is a parallelogram. Find all the other angles and find ∠B + 2∠C – 3∠D.
Answer:
∠B = 60, ∠C = 120°, ∠D = 60° and ∠B + 2∠C – 3∠D = 120
Question 10.
In the given figure, ABCD is a parallelogram, in which ZABD = 25° and ZADB = 35°. Find all the angles of the parallelogram.
Answer:
∠A = 120°, ∠B = 60°, ∠C = 120°, ∠D = 60°
Question 11.
Construct a rhombus whose length of diagonals are 8 cm and 6 cm.
Answer:
Do yourself
Question 12.
ABCD is a parallelogram as shown in figure. Find the values of x and y.
Answer:
x = 13, y = 7
Question 13.
A rectangle MORE is shown below
Answer the following questions by giving appropriate reason.
(a) Is ∠MYO = ∠RXE ?
(b) Is ∠MOY = ∠REX ?
(c) Is MY = RX ?
Answer:
(a) Yes (MY and RX are perpendicular to OE)
(b) Yes (alternate interior angles)
(c) Yes (by CPCT)
Long Answer Type Questions
Question 1.
In the given figure, ABCD is a rhombus. AEC and BED are two straight lines. Find the value of (p + q+ r + s + t).
Answer:
270°
Question 2.
A farmer’s grass field is in the form of a parallelogram PQRS. One of its animals a cow broke open and grazed in the entire field. The farmer beat it and tied it at one corner Q and reduced its grazing area. If ∠PQS = 36°, then
(a) Find all remaining angles of his grass field.
(b) Find ∠PSQ, ∠RQS and ∠RSQ.
(c) What values does the farmer lack?
Answer:
(a) ∠Q = 48°, ∠R = 132°, ∠S =48°
(b) ∠PSQ = 12°, ∠RQS =12°, ∠RSQ = 36°
(c) Farmer lacks sensitivity towards speechless animals. He lacks pity.
Question 3.
In the given parallelogram RISE, SN ⊥ RI and SM ⊥ RE. Find ∠SEM, ∠SIN and ∠NSM.
Answer:
∠SEM = 70°, ∠SIN = 70°, ∠NSM = 70°
Question 4.
RICE is a rhombus. Find x, y and z, justify your answers.
Answer:
x = 3, y = 9, z = 13
Question 5.
In the adjacent figure, both RISK and CLUE are parallelogram. Find the value of x.
Answer:
50°
Case Based Question
Question 1.
There is a trapezium MNOP, angle bisector of ∠M and ∠N meet at point W, and angle bisector of ∠O and ∠P meet at point X on side MN of trapezium MNOP.
By using the figure give the answers to following questions.
Based on the above information, answer the following questions.
(i) What is the value of a?
(a) 80°
(b) 60°
(c) 90°
(d) 70°
Answer:
(b) 60°
(ii) What is the value of d?
(a) 70°
(b) 60
(c) 80°
(d) 90
Answer:
(d) 90
(iii) What is the value of c?
(a) 90°
(b) 70
(c) 50°
(d) 80
Answer:
(a) 90°
(iv) What is the value of z?
(a) 90°
(b) 70°
(c) 50°
(d) 80°
Answer:
(a) 90°
The post Understanding Quadrilaterals Class 8 Worksheet with Answers Maths Chapter 4 appeared first on Learn CBSE.
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