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#### Question 1:

Take a point O on your notebook and draw circles of radii 4 cm, 5.3 cm and 6.2 cm, each having the same centre O. This is the required diagram as asked in the question.

#### Question 2:

Draw a circle with centre C and radius 4.5 cm. Mark points P, Q, R such taht P lies in the interior of the circle, Q lies on the circle, and R lies in the exterior of the circle. This is the required diagram as asked in the question.

#### Question 3:

Draw a circle with centre O and radius 4 cm. Draw a chord AB of the circle. Indicate by marking points X and Y, the minor arc AXB and the major arc AYB of the circle. This is the required diagram as asked in the question.

#### Question 4:

Which of the following statements are true and which are false?
(i) Each radius of a circle is also a chord of the circle.
(ii) Each diameter of a circle is also a chord of the circle.
(iii) The centre of a circle bisects each chord of the circle.
(iv) A secant of a circle is a segment having its end points on the circle.
(v) A chord of a circle is a segment having its end points on teh circle.

(i)  False
Diameter of a circle is a chord of the circle, not radius.
(ii) True
It is the longest chord of the circle.
(iii) False
A perpendicular drawn from the centre of the circle to the chord, bisects the chord.
(iv) False
It is a line passing through the circle that intersects the circle at two points.
(v) True.

#### Question 5:

Draw a circle with centre O and radius 3.7 cm. Draw a sector having the angle 72°. Therefore, the required arc is arc OACB.

#### Question 6:

Fill in the blanks by using <, >, = or ≤.
(i) OP ...... OQ, where O is the centre of the circle, P lies on the circle and Q is in the interior of the circle.
(ii) OP ...... OR, where O is the centre of the circle, P lies on the circle and R lies in the exterior of the circle.
(iii) Major arc ...... minor arc of the circle.
(iv) Major arc ...... semicircumference of the circle.

(i) >
(ii) <
(iii) >
(iv) >
This is because the major arc covers more than half of the circumference of the circle. #### Question 7:

Fill in the blanks:
(i) A diameter of a circle is a chord that .......... the centre.
(ii) A radius of a circle is a line segment with one end point ........... and the other end point ...... .
(iii) If we join any two points of a circle by a line segment, we obtain a ........... of the circle.
(iv) Any part of a circle is called an ........... of the circle.
(v) The figure bounded by an arc and the two radii joining the end points of the arc with the centre is called a ........... of the circle.

(i)  passes through
(ii)  on the circle, at the centre of the circle
(iii)  chord
(iv)  arc
(v)  sector

#### Question 1:

Define each of the following:
(a) Closed figures
(b) Open figures
(c) Polygons

(i) A closed figure is a figure that can be traced with the same starting and ending points, and that too without crossing or retracing any part of the figure.
For example: Polygon, circle, etc.

(ii) A figure having no boundary and no starting or ending points is called as an open figure.

(iii)  A polygon is a plane shape with 3 or more straight sides. It is a 2 dimensional closed figure.

#### Question 2:

Define each of the following:
(a) A scalene triangle
(b) An isosceles triangle
(c) An obtuse triangle

(a) A triangle having no sides or angles equal is called a scalene triangle.

(b) A triangle having two sides and the corresponding opposite angles equal is called an isosceles triangle.

(c) A triangle having one of the angles more than 90$°$ is called an obtuse triangle.

#### Question 3:

(i) What do you mean by a convex quadrilateral?
(ii) Define a regular polygon.

(i)  A quadrilateral with no interior angles greater than 180° is known as a convex quadrilateral.

(ii)  A regular polygon is a polygon all of whose sides are of the same lengths and all of whose interior angles are of the same measures.

#### Question 4:

The angles of a triangle are in the ratio 3 : 5 : 7. Find the measures of these angles.

The angles are in ratio 3:5:7.
Suppose the angles are 3x, 5x and 7x.

∴ 3x + 5x + 7x = 180                (angle sum property of a triangle)
15x =180
x = 12o

Therefore, the angles are of the measures 36°, 60° and 84°.

#### Question 5:

The angles of a quadrilateral are in the ratio 2 : 3 : 4 : 6. Find the measures of these angles.

Suppose the angles are 2x, 3x, 4x, and 6x.
We know that the sum of the angles of a quadrilateral is 360°.
∴ 2x + 3x + 4x + 6x = 360
15x = 360
x = 24

Therefore, the measures of the angles are 48°, 72°, 96° and 144°.

#### Question 6:

State the properties of a rhombus.

1. A rhombus is a parallelogram whose opposite sides are parallel.
2. All four of its sides are equal in length. Also, the opposite angles are equal.
3. The diagonals bisect each other at right angles.

#### Question 7:

Define (i) a trapezium (ii) a kite.

(i) A trapezium is a quadrilateral with only one pair of parallel sides.

(ii) A kite is a quadrilateral that has two pairs of equal adjacent sides, but unequal opposite sides.

#### Question 8:

Draw a circle with centre O and radius 3 cm. Draw a sector having an angle of 54°. #### Question 9:

A quadrilateral having two pairs of equal adjacent sides but unequal opposite sides is called a
(a) parallelogram
(b) rectangle
(c) trapezium
(d) kite

(d) kite

#### Question 10:

If the diagonals of a quadrilateral bisect each other at right angles, then this quadrilateral is a
(a) rectangle
(b) parallelogram
(c) rhombus
(d) kite

(c) rhombus

#### Question 11:

A quadrilateral having one and only one pair of parallel sides is called a
(a) parallelogram
(b) a kite
(c) a trapezium
(d) a rhombus

(c) a trapezium

#### Question 12:

One of the base angles of an isosceles triangle is 70°. The vertical angle is
(a) 35°
(b) 40°
(c) 70°
(d) 80°

(b) 40°

Since one base angle is 70°, the other base angle will also be 70° because the triangle is isosceles.
Vertical angle:
180 − 70 − 70 = 40$°$                 (angle sum property of a triangle)

#### Question 13:

Write 'T' for true and 'F' for false for each of the statements given below:
(i) The diagonals of a rhombus are equal.
(ii) The diagonals of a parallelogram bisect each other.
(iii) The centre of a circle bisects each chord of a circle.
(iv) Each diameter of a circle is a chord of the circle.
(v) The diagonals of a rhombus bisect each other at right angles.

(i) False
Diagonals are perpendicular and bisect each other.

(ii) True
The diagonals of a parallelogram bisect each other.

(iii) False
A perpendicular drawn from the centre of a circle to the chord, bisects the chord.

(iv)  True
It divides the circle in two equal parts.

(v) True
The diagonals of a rhombus bisect each other at right angles.

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