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Answer :

Construction according to the required data is done as follows:

Step1: Draw a line segment AB=7.6 cm and at point A draw a ray AC making acute angle with AB.

Step 2: As shown in figure, start locating 13 marks (5+8) as \(A_1,A_2,A_3,.....A_{13} \), such that \(AA_1=AA_2=AA_3 \)..and so on.

Step 3: Now join the points \(A_{13} \) and B.

Step 4: From point \(A_5 \), draw a line parallel to \(A_{13}B\) and mark the intersection point as P.

Step 5: Measure AP and PB. we will find AP= 2.9cm and PB =4.7cm(approx) which are in approx ration of 5:8.

**Justification:**

In \(ΔAA_5P and △AA_13B \) we have,

\(A_5P ∥ A_{13}B\)

\(\frac{AP}{BP}=\frac{AA_5}{A_5A_{13}} \)

(By the Basic proportionality theorem)

\(\frac{AP}{BP}=\frac{5}8 \) {∵ \(\frac{AA_5}{A_5A_{13}}=\frac{5}8 \)}

\(\therefore \) , AP:BP=5:8

- Construct a triangle of sides 4 cm, 5 cm and 6 cm and then a triangle similar to it whose sides are \(\frac{2}{3} \) of the corresponding sides of the first trianngle.
- Construct a triangle with sides 5 cm, 6 cm and 7 cm and then another triangle whose sides are \(\frac{7}{5} \) of the corresponding sides of the first triangle.
- Construct an isosceles triangle whose base is 8 cm and altitude 4 cm and then another triangle whose sides are \(1\frac { 1 }{ 2 }\) times the corresponding sides of the isosceles triangle.
- Draw a triangle ABC with side BC = 6 cm, AB = 5 cm and \(\angle \)ABC=60° ;. Then construct a triangle whose sides are \(\frac{3}4\) of the corresponding sides of the triangle ABC.
- Draw a triangle ABC with side BC = 7 cm, \(\angle \) B=45°, \(\angle \) A=105°;. Then construct a triangle whose sides are \(\frac{4}3 \) times the corresponding sides of \(\triangle \) ABC.
- 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 \(\frac{5}3\)times the corresponding sides of the given triangle.
- Q.1In each of the following, give the justification of the construction also: 1. Draw a line segment of length 7.6 cm and divide it in the ratio 5 : 8. Measure the two parts.
- Q.2 Construct a triangle of sides 4 cm, 5 cm and 6 cm and then a triangle similar to it whose sides are \(\frac{2}{3} \) of the corresponding sides of the first triangle.
- Q.3 Construct a triangle with sides 5 cm, 6 cm and 7 cm and then another triangle whose sides are \(\frac{7}{5} \) of the corresponding sides of the first triangle
- Q.4 Construct an isosceles triangle whose base is 8 cm and altitude 4 cm and then another triangle whose sides are \(1\frac{1}{2} \) times the corresponding sides of the isosceles triangle.
- Q.5 Draw a triangle ABC with side BC = 6 cm, AB = 5 cm and \(\angle \)ABC = 60°. Then construct a triangle whose sides are \(\frac{3}{4} \) of the corresponding sides of the triangle ABC.
- Q.6 Draw a triangle ABC with side BC = 7 cm, \(\angle \) B = 45°, \(\angle \) A = 105°. Then, construct a triangle whose sides are \(\frac{4}{3} \)times the corresponding sides of \(\triangle \)ABC.
- Q.7 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 \(\frac{5}{3} \) times the corresponding sides of the given triangle.

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