RS Aggrawal 2019 2020 Solutions for Class 6 Math Chapter 18 - Circles

Answer:

This is the required diagram as asked in the question.

 

Answer:

This is the required diagram as asked in the question.

Answer:

This is the required diagram as asked in the question.

Answer:

(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.

Answer:

Therefore, the required arc is arc OACB.

Answer:

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

Answer:

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

Answer:

(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.

Answer:

(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.

Answer:

(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.

Answer:

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 = 12^o

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

Answer:

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°.

Answer:

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.

Answer:

(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.

Answer:

Answer:

(d) kite

Answer:

(c) rhombus

Answer:

(c) a trapezium

Answer:

(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)

Answer:

(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.