Question

Construct \( \triangle ABC \), in which \( BC = 6 \, \text{cm} \), \( AB = 4.5 \, \text{cm} \) and \( \angle ABC = 60^\circ \). Then construct another triangle whose sides are \( \frac{3}{4} \) times the corresponding sides of \( \triangle ABC \).

Hint:

When constructing triangles with proportional sides, use the same angle and adjust the side lengths by the given ratio.

Answer 1

To construct \( \triangle ABC \):
1. Draw the base \( BC = 6 \, \text{cm} \).
2. At point \( B \), draw an angle of \( 60^\circ \) using a protractor.
3. From point \( B \), measure \( AB = 4.5 \, \text{cm} \) using a ruler and mark point \( A \).
4. Join \( A \) to \( C \) to form \( \triangle ABC \).
Now, to construct the second triangle with sides \( \frac{3}{4} \) times the corresponding sides of \( \triangle ABC \): 1. Measure the lengths of the sides of \( \triangle ABC \) (i.e., \( AB = 4.5 \, \text{cm} \), \( BC = 6 \, \text{cm} \), and \( AC \)).
2. Multiply each side by \( \frac{3}{4} \):
- New side \( AB' = \frac{3}{4} \times 4.5 = 3.375 \, \text{cm} \),
- New side \( BC' = \frac{3}{4} \times 6 = 4.5 \, \text{cm} \).
3. Using the same angle \( \angle ABC = 60^\circ \), construct the triangle by repeating the steps with the new side lengths \( AB' \) and \( BC' \).

Conclusion: You have constructed \( \triangle ABC \) and another triangle whose sides are \( \frac{3}{4} \) times the corresponding sides of \( \triangle ABC \).