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Constructions

Short Answer Type

161.

Draw a line segment of length 8 cm and divide it internally in the ratio 4: 5.
Steps of construction.

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Long Answer Type

162.

Construct an isosceles triangle with base 8 cm and altitude 4 cm. Construct another triangle whose sides are 2/3 times the corresponding sides of the isosceles triangle.

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163.

Draw a triangle ABC with BC = 6 cm, AB = 5 cm and ∠ABC 60. Then construct a triangle whose sides are 3/4 of the corresponding sides of the △ABC.

164.

Construct a tangent of a circle of radius 4 cm from a point on the concentriccircle of radius 6 cm.

165.

Draw a line segment AB of length 8 cm. Taking A as centre, draw a circle of radius 4 cm and taking B as centre, draw another circle of radius 3 cm. Construct tangents to each circle from the centre of the other circle.

166.

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

167.
Draw a triangle ABC with side BC = 6 cm, $∠$ C = 30⁰ and $∠$ A = 105⁰. Then construct another triangle whose sides are $\frac{2}{3}$ times the corresponding sides of $∆$ ABC.

$It is given that ∠ A = 105 °, ∠ C = 30 ° .$

Using angle sum propertyof triangle, we get, $∠$ B = 45⁰.

The steps of constructions are as follows:

1. Draw a line segment BC = 6 cm.

2. At B, draw a ray making an angle of 45⁰ with BC.

3. At C, draw a ray making an angle of 30⁰ with BC. Let the two rays meet at point A.

4. Below BC, make an acute $∠$ CBX. along BX mark off three points B₁, B₂, B₃. Such that BB₁ = B₁B₂ = B₂B₃. Join B₃C.

5. From B_2,draw B₂C' $∥$ B₃C.

6. From C', draw C'A' $∥$ CA, meeting BA at the point A'.

Then A'BC' is the required triangle.