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 angels of a convex quadrilateral? Will this property hold if the quadrilateral is not convex? (Make a non-convex quadrilateral and try!)

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

(a) find x + y + z

(b) find x + y + z + w

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°?

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

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

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

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

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°?

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.

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

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

Find ∠C in the following figure if 

Find the measure of ∠P and ∠S, if  in the following figure. (If you find m∠R, is there more than one method to find m∠P?)

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