Question

Construct a ΔABC in which BC = 5 cm, ∠C = 60° and altitude from A equal to 3 cm. Construct a ΔADE similar to ΔABC such that each side of ΔADE is `3/2` times the corresponding side of ΔABC. Write the steps of construction.

Answer 1

Steps of Construction:

Step 1: Draw a line l.

Step 2: Draw an angle of 90° at M on l.

Step 3: Cut an arc of radius 3 cm on the perpendicular. Mark the point as A.

Step 4: With A as centre, make an angle of 30° and let it cut l at C. We get ∠ACB = 60°.

Step 5: Cut an arc of 5 cm from C on l and mark the point as B.

Step 6: Join AB. Thus, ΔABC is obtained.

Step 7: Extend AB to D, such that BD = BC.

Step 8: Draw DE || BC, cutting AC produced to E.

 
Then, ΔADE is the required triangle, each of whose sides is of the corresponding sides of ΔABC.