Question

\( \triangle ABC \sim \triangle LMN \). In \( \triangle ABC \), \( AB = 5.5 \, \text{cm} \), \( BC = 6 \, \text{cm} \), \( CA = 4.5 \, \text{cm} \). Construct \( \triangle ABC \) and \( \triangle LMN \) such that \( \frac{BC}{MN} = \frac{5}{4} \).

Hint:

For constructing similar triangles, ensure that the scale factor is applied consistently to all sides, and corresponding angles are preserved.

Answer 1

Step 1: Construct \( \triangle ABC \):
Draw a base \( BC = 6 \, \text{cm} \).
At point \( B \), construct \( \angle ABC \) using a protractor such that \( AB = 5.5 \, \text{cm} \).
At point \( C \), construct \( \angle ACB \) using a protractor such that \( CA = 4.5 \, \text{cm} \).
Mark the point of intersection of the two arcs as \( A \), and join \( AB \) and \( AC \) to complete \( \triangle ABC \).
Step 2: Construct \( \triangle LMN \) similar to \( \triangle ABC \) with a scale factor of \( \frac{4}{5} \):
Draw a base \( MN \) such that \( MN = \frac{4}{5} \times BC = \frac{4}{5} \times 6 = 4.8 \, \text{cm} \).
At point \( M \), construct an angle equal to \( \angle ABC \).
At point \( N \), construct an angle equal to \( \angle ACB \).
Mark the point of intersection of the two arcs as \( L \), and join \( LM \) and \( LN \) to complete \( \triangle LMN \).
Step 3: Verify similarity: \[ \frac{AB}{LM} = \frac{BC}{MN} = \frac{CA}{LN} = \frac{5}{4}. \]