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Constructions

Short Answer Type

71. Construct a triangle of sides 4 cm, 5 cm and 6 cm and then a triangle similar to it whose sides arc

2 over 3

of the corresponding sides of the first triangle.

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72. Construct a triangle with sides 5 cm, 6 cm and 7 cm and then another triangle whose sides arc

7 over 5

of the corresponding sides of the first triangle.

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73. Construct an isosceles triangle whose base is 8 cm and altitude 4 cm and then another

triangle whose sides are

1 begin inline style 1 half end style

times the corres ponding sides of the isosceles triangle.

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74. Draw a triangle ABC with side BC = 6 cm, AB = 5 cm and ∠ABC = 60°. Then construct a triangle whose sides are

3 over 4

of the corresponding sides of the triangle ABC.

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75. Draw a triangle ABC with side BC = 7 cm, ∠B = 45°, ∠A = 105°. Then, construct a triangle whose sides are 4/3 times the corresponding sides of ΔABC.

Steps of Construction :
(i) Draw a triangle ABC with side BC = 7 cm, ∠B = 45°, ∠A = 105°.
(it) Draw any ray BX making an acute angle with BC on the side opposite to the vertex A.
(iii) Along BX, mark off 4 points B₁, B₂, B₃ and B₄ on BX such that BB₁ = B₁B₂ = B₂B₃ = B₃B₄(iv) Join B₃ to C and draw a line through B₄ parallel to B₃C, intersecting the extended line segment BC at C’.
(v) Draw a line through C’ parallel to CA intersecting the extended line segment BA at A’.

Steps of Construction :(i) Draw a triangle ABC with side BC = 7 cm, ?
Then A ‘BC’ is the required triangle. Justification :

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Long Answer Type

76. Draw a right triangle in which the sides (other than hypotenuse) are of lengths 4 cm and 3 cm. Then construct another triangle whose sides are

5 over 3

times the corresponding sides of the given triangle.

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Short Answer Type

77. Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct the pair of tangents to the circle and measure their lengths.

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78. Construct a tangent to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm and measure its length. Also verify the measurement by actual calculation.

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79. Draw a circle of radius 3 cm. Take two points at a distance 7 cm from its centre. Draw tangents to the circle from these two points P and Q.

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80. Draw a pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle of 60°.

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