# NCERT solutions Mathematics Textbook for Class 8 chapter 3 Understanding Quadrilaterals

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 9- 190-

### Chapter 3 - Understanding Quadrilaterals

#### 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

Q 1 | Page 44 | view solution

How many diagonals does following have?

Q 2.1 | Page 44 | view solution

How many diagonals does following have?

A regular hexagon

Q 2.2 | Page 44 | view solution

How many diagonals does following have?

A triangle

Q 2.3 | Page 44 | view solution

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!)

Q 3 | Page 44 | view solution

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

Q 4 | Page 44 | view solution

What is a regular polygon?

Q 5 | Page 42 | view solution

State the name of a regular polygon of 3 sides

Q 5.1 | Page 42 | view solution

State the name of a regular polygon of 4 sides

Q 5.2 | Page 42 | view solution

State the name of a regular polygon of 6 sides

Q 5.3 | Page 42 | view solution

Find the angle measure x in the given Figure

Q 6.1 | Page 42 | view solution

Find the angle measure x in the given Figure

Q 6.2 | Page 42 | view solution

Find the angle measure x in the given Figure

Q 6.3 | Page 42 | view solution

Find the angle measure x in the given Figure

Q 6.4 | Page 42 | view solution

Find x + y + z

Q 7.1 | Page 42 | view solution

Find x + y + z + w

Q 7.2 | Page 42 | view solution

#### Page 44

Find x in the following figures

Q 1.1 | Page 44 | view solution

Find x in the following figures.

Q 1.2 | Page 44 | view solution

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

Q 2.1 | Page 44 | view solution

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

Q 2.2 | Page 44 | view solution

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

Q 3 | Page 44 | view solution

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

Q 4 | Page 44 | view solution

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

Q 5.1 | Page 44 | view solution

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

Q 5.2 | Page 44 | view solution

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

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

Q 6 | Page 44 | view solution

#### Pages 50 - 52

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

(2) ∠DCB = …

(3) OC = …

(4) m∠DAB + m∠CDA = …

Q 1 | Page 50 | view solution

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

Q 2.1 | Page 51 | view solution

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

Q 2.2 | Page 51 | view solution

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

Q 2.3 | Page 51 | view solution

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

Q 2.4 | Page 51 | view solution

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

Q 2.5 | Page 51 | view solution

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

Q 3.1 | Page 51 | view solution

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

Q 3.2 | Page 51 | view solution

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

Q 3.3 | Page 51 | view solution

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.

Q 5 | Page 51 | view solution

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

Q 6 | Page 51 | view solution

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

Q 7 | Page 51 | view solution

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

Q 8 | Page 51 | view solution

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

Q 9 | Page 51 | view solution

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

Q 10 | Page 52 | view solution

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

Q 11 | Page 52 | view solution

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?).

Q 12 | Page 52 | view solution

#### Page 55

State whether True or False.

All rectangles are squares

Q 1.1 | Page 55 | view solution

State whether True or False.

All rhombuses are parallelograms.

Q 1.2 | Page 55 | view solution

State whether True or False

All squares are rhombuses and also rectangles.

Q 1.3 | Page 55 | view solution

State whether True or False.

All squares are not parallelograms.

Q 1.4 | Page 55 | view solution

State whether True or False.

All kites are rhombuses.

Q 1.5 | Page 55 | view solution

State whether True or False.

All rhombuses are kites.

Q 1.6 | Page 55 | view solution

State whether True or False.

All parallelograms are trapeziums.

Q 1.7 | Page 55 | view solution

State whether True or False.

All squares are trapeziums.

Q 1.8 | Page 55 | view solution

Identify all the quadrilaterals that have four sides of equal length

Q 2.1 | Page 55 | view solution

Identify all the quadrilaterals that have four right angles

Q 2.2 | Page 55 | view solution

Explain how a square is a quadrilateral

Q 3.1 | Page 55 | view solution

Explain how a square is a parallelogram

Q 3.2 | Page 55 | view solution

Explain how a square is a rhombus

Q 3.3 | Page 55 | view solution

Explain how a square is a rectangle

Q 3.4 | Page 55 | view solution

Name the quadrilaterals whose diagonals  bisect each other

Q 4.1 | Page 55 | view solution

Name the quadrilaterals whose diagonals are perpendicular bisectors of each other

Q 4.2 | Page 55 | view solution

Name the quadrilaterals whose diagonals are equal

Q 4.3 | Page 55 | view solution

Explain why a rectangle is a convex quadrilateral.

Q 5 | Page 55 | view solution

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)

Q 6 | Page 55 | view solution