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#### Chapters

1 - Rational Numbers2 - Linear Equations in One Variable

3 - Understanding Quadrilaterals

4 - Practical Geometry

5 - Data Handling

6 - Squares and Square Roots

7 - Cubes and Cube Roots

8 - Comparing Quantities

9 - Algebraic Expressions and Identities

10 - Visualising Solid Shapes

11 - Mensuration

12 - Exponents and Powers

13 - Direct and Inverse Proportions

14 - Factorisation

15 - Introduction to Graphs

16 - Playing with Numbers

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### 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

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

#### 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?

#### 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?).

#### 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)

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