Draw a triangle ABC in which AB = 4 cm, BC = 6 cm and AC = 9 cm. Construct a triangle similar to ∆ABC with scale factor `3/2`. Justify the construction. Are the two triangles congruent? Note that all the three angles and two sides of the two triangles are equal.

#### Solution

**Steps of construction**

**1.** Draw a line segment BC = 6 cm.

**2.** Taking B and C as centres, draw two arcs of radii 4 cm and 9 cm intersecting each other at A.

**3.** Join BA and CA, ΔABC is the required triangle.

**4.** From B, draw any ray BX downwards making an acute angle.

**5.** Mark three points B_{1}, B_{2}, B_{3} on BX, such that BB_{1} = B_{1}B_{2} = B_{2}B_{3}.

**6.** Join B_{2}C and from B_{3} draw B_{3}M || B_{2}C intersecting the extended line segment BC at

**7.** From point M, draw MN || CA intersecting the extended line segment BA to N.

Then, ΔNBM is the required triangle whose sides are equals to the corresponding sides of the ΔABC