Given here are some figures

(1) (2)

(3) (4)

(5) (6)

(7) (8)

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 each of the following have?

A. A convex quadrilateral

B. A regular hexagon

C. A triangle

What is the sum of the measures of the angles 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)

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

(i) 3 sides

(ii) 4 sides

(iii) 6 sides

Find the angle measure x in the following figures

A.

B.

C.

D.

A. Find x + y + z

B. Find x + y + z + w

Find x in the following figures.

A.

B.

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

(i) 9 sides

(ii) 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? Why?

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

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

(i)

(ii)

(iii)

(iv)

Consider the following parallelogram. Find the values of the unknowns x, y, z

(i)

(ii)

(iii)

(iv)

(v)

Can a quadrilateral ABCD be a parallelogram if

(i) ∠D + ∠B = 180°?

(ii) AB = DC = 8 cm, AD = 4 cm and BC = 4.4 cm?

(iii) ∠A = 70° and ∠C = 65°?

Draw a rough figure of a quadrilateral that is not a parallelogram but has exactly two opposite angles of equal measure

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)

(i)

(ii)

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? (Fig 3.32)

Find in Fig 3.33 if

Find the measure of and if in Fig 3.34.

(If you find is there more than one method to find ?)

State whether True or False

(a) All rectangles are squares

(b) All rhombuses are parallelograms

(c) All squares are rhombuses and also rectangles

(d) All squares are not parallelograms

(e) All kites are rhombuses

(f) All rhombuses are kites

(g) All parallelograms are trapeziums

(h) All squares are trapeziums

Identify all the quadrilaterals that have.

(a) Four sides of equal length

(b) Four right angles

Explain how a square is

(i) a quadrilateral

(ii) a parallelogram
(iii) a rhombus

(iv) a rectangle

Name the quadrilaterals whose diagonals

(i) Bisect each other

(ii) Are perpendicular bisectors of each other

(iii) 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).