NCERT Solutions For Class 8 Maths Chapter 4 Quadrilaterals

NCERT Solutions for Class 8 Maths Chapter 4 Quadrilaterals helps students understand four-sided closed figures and their properties. This chapter explains different types of quadrilaterals such as rectangle, square, parallelogram, rhombus, trapezium, and kite. Students learn about sides, angles, diagonals, symmetry, and angle sum property. These concepts are very useful in geometry, mensuration, and higher mathematics. Regular practice of this chapter improves diagram understanding, logical thinking, and problem-solving skills.

Question & Answers

Q1. How many sides does a quadrilateral have?

Answer: A quadrilateral has 4 sides.

NCERT Solutions For Class 8 Maths Chapter 4 Quadrilaterals

Quadrilaterals (New NCERT)
Medium
Q.
Find all the other angles inside the following rectangles.
Quadrilaterals (New NCERT)
Medium
Q.
Find the remaining angles in the following trapeziums.
Quadrilaterals (New NCERT)
Medium
Q.
Will the sum of the angles in a quadrilateral, such as the following one, also be 360°? Find the answer using geometric reasoning as well as by constructing this figure and measuring.
Quadrilaterals (New NCERT)
Medium
Q.
What type of quadrilateral is one in which the opposite sides are equal? Justify your answer.
Hint: Draw a diagonal and check for congruent triangles.
Quadrilaterals (New NCERT)
Medium
Q.
If a quadrilateral has four equal sides and one angle of 90°, will it be a square? Find the answer using geometric reasoning as well as by construction and measurement.
Quadrilaterals (New NCERT)
Medium
Q.
CASE is a square. The points U, V, W, and X are the midpoints of the sides of the square. What type of quadrilateral is UVWX? Find this by using geometric reasoning, as well as by construction and measurement. Find other ways of constructing a square within a square such that the vertices of the inner square lie on the sides of the outer square, as shown in Figure (b).
Quadrilaterals (New NCERT)
Medium
Q.
Construct a square with a diagonal of 6 cm without using a protractor.
Quadrilaterals (New NCERT)
Medium
Q.
If PAIR and RODS are two rectangles, find ∠IOD.
Quadrilaterals (New NCERT)
Medium
Q.
Draw a Venn diagram showing the set of parallelograms, kites, rhombuses, rectangles, and squares. Then answer the following questions.
(i) What is the quadrilateral that is both a kite and a parallelogram?
(ii) Can there be a quadrilateral that is both a kite and a rectangle?
(iii) Is every kite a rhombus? If not, what is the correct relationship between these two types of quadrilaterals?
Quadrilaterals (New NCERT)
Medium
Q.
Construct a kite whose diagonals are of lengths 6 cm and 8 cm.
Quadrilaterals (New NCERT)
Medium
Q.
Draw a quadrilateral whose diagonals have equal lengths of 8 cm that bisect each other, and intersect at an angle of:
(i) 30°
(ii) 40°
(iii) 90°
(iv) 140°
Quadrilaterals (New NCERT)
Medium
Q.
​Find all the sides and the angles of the quadrilateral obtained by joining two equilateral triangles with sides 4 cm.​
Quadrilaterals (New NCERT)
Medium
Q.
Using the diagonal properties, construct a rhombus whose diagonals are of lengths 4 cm and 5 cm.
Quadrilaterals (New NCERT)
Medium
Q.
Using the diagonal properties, construct a parallelogram whose diagonals are of lengths 7 cm and 5 cm, and intersect at an angle of 140°.
Quadrilaterals (New NCERT)
Medium
Q.
Find the remaining angles in the following quadrilaterals.
Quadrilaterals (New NCERT)
Medium
Q.
We saw that one of the properties of a rectangle is that its opposite sides are parallel. Can this be chosen as a definition of a rectangle? In other words, is every quadrilateral that has opposite sides parallel and equal a rectangle?
Quadrilaterals (New NCERT)
Medium
Q.
We have seen how to get 90° using paper folding. Now, suppose we do not have any paper but two sticks of equal length and a thread. How do we make an exact 90° angle using these?
Quadrilaterals (New NCERT)
Medium
Q.
Consider a circle with centre O. Line segments PL and AM are two perpendicular diameters of the circle. What is the figure APML? Reason and/or experiment to figure this out.
Quadrilaterals (New NCERT)
Medium
Q.
State whether the following statements are true or false. Justify your answers.
(i) A quadrilateral whose diagonals are equal and bisect each other must be a square.
(ii) A quadrilateral having three right angles must be a rectangle.
(iii) A quadrilateral whose diagonals bisect each other must be a parallelogram.
(iv) A quadrilateral whose diagonals are perpendicular to each other must be a rhombus.
(v) A quadrilateral in which the opposite angles are equal must be a parallelogram.
(vi) A quadrilateral in which all the angles are equal is a rectangle.
(vii) Isosceles trapeziums are parallelograms.

NCERT Solutions For Class 8 Maths Chapter 4 Quadrilaterals

Q2. Find the missing angle of a quadrilateral if three angles are 80°, 90°, and 100°.

Answer:
Missing angle = 360° - (80° + 90° + 100°)
= 360° - 270°
= 90°

Q3. State whether true or false:

(i) All squares are rectangles.

Answer: True

(ii) All rectangles are squares.

Answer: False

(iii) Opposite sides of parallelogram are equal.

Answer: True

Q4. Name the quadrilateral:

(i) Four equal sides and four right angles

Answer: Square

(ii) Opposite sides equal and parallel

Answer: Parallelogram

(iii) One pair of opposite sides parallel

Answer: Trapezium

Q5. What is the sum of interior angles of a quadrilateral?

Answer: 360°

Q6. Which quadrilateral has only one pair of parallel sides?

Answer: Trapezium

Q7. Which quadrilateral has all sides equal but angles not necessarily 90°?

Answer: Rhombus

Q8. What shape has opposite sides equal and all angles 90°?

Answer: Rectangle

Q9. How many diagonals does a quadrilateral have?

Answer: A quadrilateral has 2 diagonals.

Q10. Which quadrilateral has four equal sides and four right angles?

Answer: Square

FAQs

1. What is Chapter 4 of Class 8 Maths?

Chapter 4 of Class 8 Maths is Quadrilaterals, based on four-sided figures and their properties.

2. Why is this chapter important?

It builds the base for geometry, shapes, constructions, and mensuration.

3. What is the angle sum of a quadrilateral?

The sum of all interior angles of a quadrilateral is 360°.

4. What is a square?

A square is a quadrilateral with four equal sides and four right angles.