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NCERT solutions for Class 8 Mathematics chapter 3 - Understanding Quadrilaterals

Mathematics Textbook for Class 8

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NCERT Mathematics Class 8

Mathematics Textbook for Class 8 - Shaalaa.com

Chapter 3: Understanding Quadrilaterals

Ex. 3.10Ex. 3.20Ex. 3.30Ex. 3.40

Chapter 3: Understanding Quadrilaterals Exercise 3.10 solutions [Pages 41 - 42]

Ex. 3.10 | Q 1 | Page 41

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

Ex. 3.10 | Q 2.1 | Page 41

How many diagonals does following have?

A convex quadrilateral

Ex. 3.10 | Q 2.2 | Page 41

How many diagonals does following have?

A regular hexagon

Ex. 3.10 | Q 2.3 | Page 41

How many diagonals does following have?

A triangle

Ex. 3.10 | Q 3 | Page 41

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!)

Ex. 3.10 | Q 4 | Page 41

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

 

Ex. 3.10 | Q 5.1 | Page 42

What is a regular polygon?

Ex. 3.10 | Q 5.2 | Page 42

State the name of a regular polygon of 3 sides

Ex. 3.10 | Q 5.3 | Page 42

State the name of a regular polygon of 4 sides

Ex. 3.10 | Q 5.4 | Page 42

State the name of a regular polygon of 6 sides

Ex. 3.10 | Q 6.1 | Page 42

Find the angle measure x in the given Figure

Ex. 3.10 | Q 6.2 | Page 42

Find the angle measure x in the given Figure

Ex. 3.10 | Q 6.3 | Page 42

Find the angle measure x in the given Figure

Ex. 3.10 | Q 6.4 | Page 42

Find the angle measure x in the given Figure

Ex. 3.10 | Q 7.1 | Page 42

Find x + y + z

Ex. 3.10 | Q 7.2 | Page 42

Find x + y + z + w

Chapter 3: Understanding Quadrilaterals Exercise 3.20 solutions [Page 44]

Ex. 3.20 | Q 1.1 | Page 44

Find x in the following figures

Ex. 3.20 | Q 1.2 | Page 44

Find x in the following figures.

Ex. 3.20 | Q 2.1 | Page 44

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

Ex. 3.20 | Q 2.2 | Page 44

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

Ex. 3.20 | Q 3 | Page 44

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

Ex. 3.20 | Q 4 | Page 44

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

Ex. 3.20 | Q 5.1 | Page 44

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

Ex. 3.20 | Q 5.2 | Page 44

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

Ex. 3.20 | Q 6 | Page 44

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 Exercise 3.30 solutions [Pages 50 - 52]

Ex. 3.30 | Q 1 | Page 50

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 = …

Ex. 3.30 | Q 2.1 | Page 51

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

Ex. 3.30 | Q 2.2 | Page 51

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

Ex. 3.30 | Q 2.3 | Page 51

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

Ex. 3.30 | Q 2.4 | Page 51

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

Ex. 3.30 | Q 2.5 | Page 51

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

Ex. 3.30 | Q 3.1 | Page 51

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

Ex. 3.30 | Q 3.2 | Page 51

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

Ex. 3.30 | Q 3.3 | Page 51

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

Ex. 3.30 | Q 5 | Page 51

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.

Ex. 3.30 | Q 6 | Page 51

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

Ex. 3.30 | Q 7 | Page 51

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

Ex. 3.30 | Q 8 | Page 51

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

Ex. 3.30 | Q 9 | Page 51

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

Ex. 3.30 | Q 10 | Page 52

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

Ex. 3.30 | Q 11 | Page 52

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

Ex. 3.30 | Q 12 | Page 52

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 Exercise 3.40 solutions [Page 55]

Ex. 3.40 | Q 1.1 | Page 55

State whether True or False.

All rectangles are squares

  • True

  • False

Ex. 3.40 | Q 1.2 | Page 55

State whether True or False.

All rhombuses are parallelograms.

  • True

  • False

Ex. 3.40 | Q 1.3 | Page 55

State whether True or False

All squares are rhombuses and also rectangles.

  • True

  • False

Ex. 3.40 | Q 1.4 | Page 55

State whether True or False.

All squares are not parallelograms.

  • True

  • False

Ex. 3.40 | Q 1.5 | Page 55

State whether True or False.

All kites are rhombuses.

  • True

  • False

Ex. 3.40 | Q 1.6 | Page 55

State whether True or False.

All rhombuses are kites.

  • True

  • False

Ex. 3.40 | Q 1.7 | Page 55

State whether True or False.

All parallelograms are trapeziums.

  • True

  • False

Ex. 3.40 | Q 1.8 | Page 55

State whether True or False.

All squares are trapeziums.

  • True

  • False

Ex. 3.40 | Q 2.1 | Page 55

Identify all the quadrilaterals that have four sides of equal length

Ex. 3.40 | Q 2.2 | Page 55

Identify all the quadrilaterals that have four right angles

Ex. 3.40 | Q 3.1 | Page 55

Explain how a square is a quadrilateral

Ex. 3.40 | Q 3.2 | Page 55

Explain how a square is a parallelogram

Ex. 3.40 | Q 3.3 | Page 55

Explain how a square is a rhombus

Ex. 3.40 | Q 3.4 | Page 55

Explain how a square is a rectangle

Ex. 3.40 | Q 4.1 | Page 55

Name the quadrilaterals whose diagonals  bisect each other

Ex. 3.40 | Q 4.2 | Page 55

Name the quadrilaterals whose diagonals are perpendicular bisectors of each other

Ex. 3.40 | Q 4.3 | Page 55

Name the quadrilaterals whose diagonals are equal

Ex. 3.40 | Q 5 | Page 55

Explain why a rectangle is a convex quadrilateral.

Ex. 3.40 | Q 6 | Page 55

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

Ex. 3.10Ex. 3.20Ex. 3.30Ex. 3.40

NCERT Mathematics Class 8

Mathematics Textbook for Class 8 - Shaalaa.com

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 Regular and Irregular Polygons, Angle Sum Property, Sum of the Measures of the Exterior Angles of a Polygon, Concept of Trapezium, Concept of Kite, Elements of a Parallelogram, Diagonals of a Parallelogram, Concept of Rhombus, Concept of a Rectangle, Classification of Polygons, Concept of Diagonals, Convex and Concave Polygons, Introduction of Quadrilaterals, Concept of a Square, 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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