#### Chapters

Chapter 2: Linear Equations in One Variable

Chapter 3: Understanding Quadrilaterals

Chapter 4: Practical Geometry

Chapter 5: Data Handling

Chapter 6: Squares and Square Roots

Chapter 7: Cubes and Cube Roots

Chapter 8: Comparing Quantities

Chapter 9: Algebraic Expressions and Identities

Chapter 10: Visualising Solid Shapes

Chapter 11: Mensuration

Chapter 12: Exponents and Powers

Chapter 13: Direct and Inverse Proportions

Chapter 14: Factorisation

Chapter 15: Introduction to Graphs

Chapter 16: Playing with Numbers

## Chapter 3: Understanding Quadrilaterals

### NCERT solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Exercise 3.1 [Pages 41 - 42]

Given here are some figures

Classify each of them on the basis of the following

(a) Simple curve

(b) Simple closed curve

(c) Polygon

(d) Convex polygon

(e) Concave polygon

How many diagonals does following have?

A convex quadrilateral

How many diagonals does following have?

A regular hexagon

How many diagonals does following have?

A triangle

What is the sum of the measures of the angels of a convex quadrilateral? Will this property hold if the quadrilateral is not convex? (Make a non-convex quadrilateral and try!)

Examine the table. (Each figure is divided into triangles and the sum of the angles deduced from that.)

Figure |
||||

Side |
3 | 4 | 5 | 6 |

Angle sum |
180° |
2 × 180° = (4 − 2) × 180° |
3 × 180° = (5 − 2) × 180° |
4 × 180° = (6 − 2) × 180° |

What can you say about the angle sum of a convex polygon with number of sides?

a) 7

b) 8

c) 10

d) n

What is a regular polygon?

State the name of a regular polygon of 3 sides

State the name of a regular polygon of 4 sides

State the name of a regular polygon of 6 sides

Find the angle measure x in the given Figure

Find the angle measure x in the given Figure

Find the angle measure x in the given Figure

Find the angle measure x in the given Figure

Find x + y + z

Find x + y + z + w

### NCERT solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Exercise 3.2 [Page 44]

Find *x* in the following figures

Find *x* in the following figures.

Find the measure of each exterior angle of a regular polygon of 9 sides

Find the measure of each exterior angle of a regular polygon of 15 sides

How many sides does a regular polygon have if the measure of an exterior angle is 24°?

How many sides does a regular polygon have if each of its interior angles is 165°?

Is it possible to have a regular polygon with measure of each exterior angle as 22°?

Can it be an interior angle of a regular polygon? Why?

What is the minimum interior angle possible for a regular polygon?

What is the maximum exterior angle possible for a regular polygon?

### NCERT solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Exercise 3.3 [Pages 50 - 52]

Given a parallelogram ABCD. Complete each statement along with the definition or property used.

(1) AD = …

(2) ∠DCB = …

(3) OC = …

(4) *m*∠DAB +* m*∠CDA = …

Consider the given parallelograms. Find the values of the unknowns x, y, z.

Consider the given parallelograms. Find the values of the unknowns x, y, z.

Consider the given parallelograms. Find the values of the unknowns x, y, z.

Consider the given parallelograms. Find the values of the unknowns x, y, z.

Consider the given parallelograms. Find the values of the unknowns x, y, z.

Can a quadrilateral ABCD be a parallelogram if ∠D + ∠B = 180°?

Can a quadrilateral ABCD be a parallelogram if AB = DC = 8 cm, AD = 4 cm and BC = 4.4 cm?

Can a quadrilateral ABCD be a parallelogram if ∠A = 70° and ∠C = 65°?

The measures of two adjacent angles of a parallelogram are in the ratio 3:2. Find the measure of each of the angles of the parallelogram.

Two adjacent angles of a parallelogram have equal measure. Find the measure of each of the angles of the parallelogram.

The adjacent figure HOPE is a parallelogram. Find the angle measures *x*, *y* and* z*. State the properties you use to find them.

The following figures GUNS is parallelograms. Find x and y. (Lengths are in cm)

The following figures RUNS is parallelograms. Find x and y. (Lengths are in cm)

In the above figure both RISK and CLUE are parallelograms. Find the value of *x*.

Explain how this figure is a trapezium. Which of its two sides are parallel?

Find *m*∠C in the following figure if `bar(AB) || bar(DC)`

Find the measure of ∠P and ∠S, if `bar(SP) || bar(RQ)` in the following figure. (If you find *m*∠R, is there more than one method to find *m*∠P?).

### NCERT solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Exercise 3.4 [Page 55]

State whether True or False.

All rectangles are squares

True

False

State whether True or False.

All rhombuses are parallelograms.

True

False

State whether True or False

All squares are rhombuses and also rectangles.

True

False

State whether True or False.

All squares are not parallelograms.

True

False

State whether True or False.

All kites are rhombuses.

True

False

State whether True or False.

All rhombuses are kites.

True

False

State whether True or False.

All parallelograms are trapeziums.

True

False

State whether True or False.

All squares are trapeziums.

True

False

Identify all the quadrilaterals that have four sides of equal length

Identify all the quadrilaterals that have four right angles

Explain how a square is a quadrilateral

Explain how a square is a parallelogram

Explain how a square is a rhombus

Explain how a square is a rectangle

Name the quadrilaterals whose diagonals bisect each other

Name the quadrilaterals whose diagonals are perpendicular bisectors of each other

Name the quadrilaterals whose diagonals are equal

Explain why a rectangle is a convex quadrilateral.

ABC is a right-angled triangle and O is the mid point of the side opposite to the right angle. Explain why O is equidistant from A, B and C. (The dotted lines are drawn additionally to help you)

## Chapter 3: Understanding Quadrilaterals

## NCERT solutions for Class 8 Maths chapter 3 - Understanding Quadrilaterals

NCERT solutions for Class 8 Maths chapter 3 (Understanding Quadrilaterals) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Class 8 Maths solutions in a manner that help students grasp basic concepts better and faster.

Further, we at Shaalaa.com provide such solutions so that students can prepare for written exams. NCERT textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

Concepts covered in Class 8 Maths chapter 3 Understanding Quadrilaterals are Properties of Trapezium, Angle Sum Property of a Quadrilateral, Properties of Kite, Classification of Polygons, Properties of a Parallelogram, Concept of Curves, Different Types of Curves - Closed Curve, Open Curve, Simple Curve., Concept of Polygons - Side, Vertex, Adjacent Sides, Adjacent Vertices and Diagonal, Interior Angles of a Polygon, Exterior Angles of a Polygon and Its Property, Concept of Quadrilaterals - Sides, Adjacent Sides, Opposite Sides, Angle, Adjacent Angles and Opposite Angles, Property: The diagonals of a rhombus are perpendicular bisectors of one another., Properties of Rhombus, Property: The Opposite Sides of a Parallelogram Are of Equal Length., Property: The Opposite Angles of a Parallelogram Are of Equal Measure., Property: The adjacent angles in a parallelogram are supplementary., Property: The diagonals of a parallelogram bisect each other. (at the point of their intersection), Property: The Diagonals of a Rectangle Are of Equal Length., Properties of Rectangle, Properties of a Square, Property: The diagonals of a square are perpendicular bisectors of each other..

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