Question

Write the steps to follow to construct a triangle with sides 5cm and 6cm with the included angle ${60}^{\circ }$. Then, construct a triangle with the corresponding sides in the ratio 7:9.

Answer 1

1. Draw any triangle with base BC .
2. From B, draw a ray BX. Cut 9 arcs of equal length on the ray BX at $B_1,B_2,..B_9$.
3. Draw a line from $B_7$ to C.
4. From $B_9$, draw another line parallel to $B_{7}C$, cutting the extended line BC at $C_1$.
5. From $C_1$, draw another line parallel to AC, cutting the extended line BA at $A_1$.
Triangle $A_{1}B{C}_1$ is the required similar triangle to ABC with the ratio of corresponding sides 7:9.