- Introduction
- Exercise 2.1 - part 1
- Exercise Problems-2.1 - Part 2
- Exercise 2.2
- Exercise 2.3- part 1
- Exercise 2.3 - part 2
- Algebraic Identities
- Example Problems-2.4
- Exercise 2.4 - part 1
- Exercise Problems 2.4 - part 2
- Exercise Problems 2.4 - part 3
- Exercise 2.5 - Part 1
- Exercise Problems 2.5 - part 2
- Introduction
- Surface Area and Volume of a Cube
- Surface Area and volume of a Cuboid
- Surface Area and Volume of a Right Circular Cylinder
- Surface Area and Volume of a Hollow Right Circular Cylinder
- Surface Area and Volume of a Right Circular Cone
- Surface Area and Volume of a Sphere
- Surface Area and Volume of a Hemisphere
- Exercise 10.1
Exercise 13.1
Exercise 13.1
1. Construct the following angles at the initial point of a given ray and justify the construction.
(a) 90^{\circ}
(b) 45^{\circ}
Sol:
(a) 90^{\circ}
Fig
1. Let AB be the given ray.
2. produce BA to D
3. Taking A as center draw a semi-circle with some radius.
4. With X and Y as center draw two intersecting arcs of the same radius.
(b) 45^{\circ}
Fig
1. Construct 90^{\circ}
2. Bisect it from ∠BAD = 45^{\circ}
2. Construct the following angles using ruler and compass and verify by measuring them by a protractor.
(a) 30^{\circ}
(b) 22\frac{1}{2}^{\circ}
(c) 15^{\circ}
(d) 75^{\circ}
(e) 105^{\circ}
f) 135^{\circ}
Sol:
(a) 30^{\circ}
Fig
Construct ∠ABY = 60^{\circ}
Bisect ∠ABY, such that ∠ABC = ∠CBY = 30^{\circ}
(b) 22\frac{1}{2}^{\circ}
Fig
Construct ∠ABD = 90^{\circ}
Bisect ∠ABD, such that ∠ABC = ∠CBD = 45^{\circ}
Bisect ∠ABC such that ∠ABE = ∠EBC = 22\frac{1}{2}^{\circ}
(c) 15^{\circ}
Fig
Construct ∠BAE = 60^{\circ}
Bisect ∠BAE such that ∠BAC = ∠CAE = 30^{\circ}
Bisect ∠BAC such that ∠BAF = ∠FAC = 15^{\circ}
(d) 75^{\circ}
Fig
Construct ∠BAC = 60^{\circ}
Construct ∠CAD = 60^{\circ}
Bisect ∠CAD such that ∠BAE = 90^{\circ}
Bisect ∠CAE such that ∠BAF = 75^{\circ}
(e) 105^{\circ}
Fig
Construct ∠ABC = 90^{\circ}
Construct ∠CBE = 30^{\circ}
Bisect ∠CBE such that the angle formed ∠ABD = 105^{\circ}
f) 135^{\circ}
Fig
Construct ∠ABC = 120^{\circ}
Construct ∠CBD = 30^{\circ}
Bisect ∠CBE such that the angle formed ∠ABE = 135^{\circ}
3. Construct an equilateral triangle, given its side of length of 4.5 cm and justify the construction.
Sol:
Fig
Steps:
1. Draw a line segment AB = 4.5 cm
2. With B and A as centers draw two arcs of radius 4.5 cm meeting at C.
3. Join C to A and B
4. ΔABC is the required triangle.
4. Construct an isosceles triangle, given its base and base angle and justify the construction.
[Hint: You can take any measure of side and angle]
Sol:
Fig
Steps:
1. Draw a line segment AB of any given length.
2. Construct ∠BAX and ∠ABY at A and B such that ∠A = ∠B.
3. Ax and BY will intersect at C.
4. ΔABC is the required triangle.
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