Question

Construct a triangle of sides 4 cm, 5 cm, and 6 cm, and again construct another corresponding triangle whose sides are \( \frac{2}{3} \) of the corresponding sides of the previous triangle.

Hint:

When constructing a similar triangle, maintain the angles and scale the side lengths proportionally based on the required factor.

Answer 1

Step 1: Draw the triangle with sides 4 cm, 5 cm, and 6 cm.
1. Draw a line segment of length 6 cm.
2. Using a protractor, draw an angle of \( \angle A = \) (appropriate angle based on the sides 4 cm and 5 cm).
3. Using a ruler, mark the other two sides, 4 cm and 5 cm, with the correct angles, forming a triangle.
Step 2: Construct the second triangle with sides \( \frac{2}{3} \) of the corresponding sides of the first triangle.
1. To construct the second triangle, multiply each of the sides of the original triangle by \( \frac{2}{3} \). - \( \frac{2}{3} \times 4 \, \text{cm} = 2.67 \, \text{cm} \)
- \( \frac{2}{3} \times 5 \, \text{cm} = 3.33 \, \text{cm} \)
- \( \frac{2}{3} \times 6 \, \text{cm} = 4 \, \text{cm} \)
2. Now, repeat the process of constructing a triangle with these new side lengths (2.67 cm, 3.33 cm, and 4 cm) using the same method as in Step 1, ensuring the angles between the sides remain the same.

Conclusion:
The second triangle will have side lengths 2.67 cm, 3.33 cm, and 4 cm, and it will be similar to the first triangle.