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Answer :

Steps of construction by the given data are:

Step 1. Draw a \(\triangle \) ABC with sides as AB=5 cm, BC= 7 cm, AC= 6cm.

Step 2. At point B, draw an acute angle CBX below BC.

Step 4. Join \(B_5\) and C.

Step 5.Draw \(B_7C'\) parallel to \(B_5C\), where C` is a point on extended line BC.

Step 6. Draw A'C' parallel to AC, where A' is a point on extended line BA.

Hence,A’BC’ is the required triangle.

**JUSTIFICATION:**

In \(\triangle \) ABC and \(\triangle \) A’BC’,

AC || A’C’

\(\frac{AB}{A’B}=\frac{BC}{BC’}\)

(By the basic Proportionality Theorem)...(i)

In \(ΔBB_5C \)and \(ΔBB_7C’\),

\(B_5C || B_7C’\)

\(\frac{BC}{BC’}=\frac{BB_5}{BB_7}=\frac{5}7\) (By the basic Proportionality Theorem)...(ii)

Equating (i) and (ii) \(\frac{AB}{A’B}=\frac{BB_5}{BB_7} \Rightarrow \frac{AB}{A’B}=\frac{5}7 \)

\(\therefore A’B=\frac{7}5AB\)

\(\therefore \) Sides of new triangle is \(\frac{7}5 \)times the corresponding sides of the first triangle.

- Draw a line segment of length 7.6 cm and divide it in the ratio 5:8. Measure the two parts.
- 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 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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