#### 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

#### NCERT Mathematics Class 8

## Chapter 3: Understanding Quadrilaterals

#### Chapter 3: Understanding Quadrilaterals solutions [Pages 42 - 44]

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

#### Chapter 3: Understanding Quadrilaterals solutions [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?

#### Chapter 3: Understanding Quadrilaterals solutions [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 and RUNS are 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?).

#### Chapter 3: Understanding Quadrilaterals solutions [Page 55]

State whether True or False.

All rectangles are squares

State whether True or False.

All rhombuses are parallelograms.

State whether True or False

All squares are rhombuses and also rectangles.

State whether True or False.

All squares are not parallelograms.

State whether True or False.

All kites are rhombuses.

State whether True or False.

All rhombuses are kites.

State whether True or False.

All parallelograms are trapeziums.

State whether True or False.

All squares are trapeziums.

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)

#### NCERT Mathematics Class 8

#### Textbook solutions for Class 8

## NCERT solutions for Class 8 Mathematics 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 Mathematics Textbook for Class 8 solutions in a manner that help students grasp basic concepts better and faster.

Further, we at shaalaa.com are providing 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 Mathematics chapter 3 Understanding Quadrilaterals are Concept of a Square, Convex and Concave Polygons, Concept of Diagonals, Classification of Polygons, Introduction of Quadrilaterals, Concept of a Rectangle, Concept of Rhombus, Diagonals of a Parallelogram, Elements of a Parallelogram, Concept of Kite, Concept of Trapezium, Sum of the Measures of the Exterior Angles of a Polygon, Angle Sum Property, Regular and Irregular Polygons, Concept of Parallelogram.

Using NCERT Class 8 solutions Understanding Quadrilaterals exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in NCERT Solutions are important questions that can be asked in the final exam. Maximum students of CBSE Class 8 prefer NCERT Textbook Solutions to score more in exam.

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