# 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. Construct a __line segment__ BC = 6 cm

2. Taking B as centre and 4 cm __radius__, construct an arc

3. Taking C as centre and 9 cm radius, construct another arc intersecting the previous arc at A

4. Now join BA and CA. ∆ABC is the required triangle

5. Through the point B, construct an acute angle ∠CBX on the side opposite to the vertex A

6. Mark three arcs B_{1}, B_{2} and B_{3} on BX where BB_{1} = B_{1}B_{2} = B_{2}B_{3}

7. Join B_{2}C

8. Construct B_{3}C’||B_{2}C which intersects the extended line segment BC at the point C’

9. Construct C’A’ || CA which intersects the extended line segment BA at the point A’

∆A’BC’ is the required triangle

Justification:

We know that

B_{3}C’ || B_{2}C

BC/CC’ = 2/1

Here

BC’/BC = (BC + CC’)/BC = 1 + CC’/BC

= 1 + 1/2

= 3/2

Similarly

CC’||CA

∆ABC is similar to ∆A’BC’

A’B/AB = BC’/BC = CC’/AC = 3/2

Therefore, the two triangles are not congruent.

**✦ Try This: **Draw a triangle ABC in which AB = 2 cm, BC = 3 cm and AC = 10 cm. Construct a triangle similar to ∆ABC with scale factor 2/3. Justify the construction. Are the two triangles congruent? Note that all the three angles and two sides of the two triangles are equal.

**☛ Also Check:** NCERT Solutions for Class 10 Maths Chapter 11

**NCERT Exemplar Class 10 Maths Exercise 10.4 Problem 7**

## 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

**Summary:**

A triangle ABC with AB = 4 cm, BC = 6 cm and AC = 9 cm is drawn. A triangle similar to ∆ABC with scale factor 3/2 is constructed. No, the two triangles are not congruent

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