Question

Draw ΔRSP ∼ ΔTQP. In ΔTQP, TP = 5 cm, ∠P = 50°, PQ = 4.5 cm and `("RS")/("TQ") = 2/3`.

Answer 1

Steps of construction:

1. Draw segment PQ = 4.5 cm.
2. Draw ray PX such that ∠XPQ = 50°.
3. Take point T on ray PX such that PT = 5 cm.
4. Join TQ. ΔTQP is obtained.
5. Divide segment PQ into 3 equal parts.
6. Fix point S on PQ such that the length of PS is `2/3` of the length of segment PQ.
7. Draw a line parallel to side TQ through S.
8. Name the point of intersection of the line and ray PT as R. Thus, we get the required ΔRSP similar to ΔTQP.