Question 1

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

Question 2

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!)

Question 3

How many diagonals does each of the following have?

(b) A regular hexagon

(c) A triangle

Question 4

Explain why a rectangle is a convex quadrilateral.

Question 5

What is a regular polygon?

State the name of a regular polygon of

(i) 3 sides

(ii) 4 sides

(iii) 6 sides

Question 6

How many diagonals does each of the following have?

(b) A regular hexagon

(c) A triangle

Question 7

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!)

Question 8

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

Question 9

Find the angle measure x in the following figures.

 (a) (b) (c) (d)

Question 10

(a) find x + y + z

(b) find x + y + z + w

Question 11

The angles of quadrilateral are in the ratio 3: 5: 9: 13. Find all the angles of the quadrilateral.

Question 12

Find x in the following figures.

 (a) (b)

Question 13

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

(i) 9 sides

(ii) 15 sides

Question 14

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

Question 15

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

Question 16

(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?

Question 17

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

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

Question 18

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

Question 19

Identify all the quadrilaterals that have

(a) four sides of equal length

(b) four right angles

Question 20

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

(ii) ∠DCB = …

(iii) OC = …

(iv) m∠DAB + m∠CDA = …

Question 21

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°?

Question 22

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

Question 23

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

 (i) (ii)

Question 24

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.

Question 25

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

(ii) ∠DCB = …

(iii) OC = …

(iv) m∠DAB + m∠CDA = …

Question 26

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

 (i) (ii) (iii) (iv) (v)

Question 27

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°?

Question 28

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

Question 29

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.

Question 30

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

Question 31

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

Question 32

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

Question 33

In the given figure, if TP and TQ are the two tangents to a circle with centre O so that ∠POQ = 110, then ∠PTQ is equal to

(A) 60 (B) 70

(C) 80 (D) 90

Question 34

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

(ii) ∠DCB = …

(iii) OC = …

(iv) m∠DAB + m∠CDA = …

Question 35

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

 (i) (ii)

Question 36

(i) bisect each other

(ii) are perpendicular bisectors of each other

(iii) are equal

Question 37

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.

Question 38

(i) bisect each other

(ii) are perpendicular bisectors of each other

(iii) are equal

Question 39

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).

Question 40

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.

Question 41

(i) bisect each other

(ii) are perpendicular bisectors of each other

(iii) are equal

Question 42

Explain why a rectangle is a convex quadrilateral.

Question 43

Explain how a square is.

(ii) a parallelogram

(iii) a rhombus

(iv) a rectangle

Question 44

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.

Question 45