# Draw a triangle ABC in which AB = 5 cm, BC = 6 cm and ∠ABC = 60º . Construct a triangle similar to ∆ ABC with scale factor 5/7. Justify the construction

**Solution:**

Steps of Construction

1. Construct a __line segment__ AB = 5 cm

2. From the point B, construct ∠ABC =60º

In order to find angle B

(i) Taking B as centre and with any radius construct another arc which cuts the line AB at D

(ii) Taking D as centre and with same __radius__ construct the first arc at the point E

(iii) Construct a ray BY which passes through E and forms an angle 60º with the line AB

3. Taking B as centre and radius 6 cm construct an arc which intersects the line BY at C

4. Join AC and triangle ABC is the required triangle.

5. From the point A, construct any ray AX downwards which makes an __acute angle__

6. Locate 7 points A_{1}, A_{2}, A_{3}, A_{4}, A_{5}, A_{6} and A_{7} on AX where AA_{1} = A_{1}A_{2} = A_{2}A_{3} = A_{3}A_{4} = A_{4}A_{5} = A_{5}A_{6} = A_{6}A_{7}

7. Join A_{7}B and from the point A_{5} construct A_{5}M||A_{7}B which intersects AB at M

8. From M construct MN||BC which intersects AC at N.

∆ AMN is the required triangle whose sides are equal to 5/7 of its __corresponding sides__ of ∆ABC.

Justification:

Consider AA_{1} = A_{1}A_{2} = A_{2}A_{3} = A_{3}A_{4} = A_{4}A_{5} = A_{5}A_{6} = A_{6}A_{7} = x

From the construction

A_{5}M || A_{7}B

AM/MB = AA_{5}/A_{5}A_{7} = 5x/2x = 5/2

AM/MB = 5/2

We know that

AB/AM = (AM + MB)/AM = AM/AM + MB/AM

= 1 + 2/5

= 7/5

Here MN || BC

r AMC is congruent to r AMN

So we get

AN/AC = NM/BC = AM/AB = 5/7

Therefore, a triangle similar to ∆ ABC with scale factor 5/7 is constructed.

**✦ Try This: **Draw a triangle ABC in which AB = 2 cm, BC = 3 cm and ∠ABC =30º . Construct a triangle similar to ∆ ABC with scale factor 6/7. Justify the construction.

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

**NCERT Exemplar Class 10 Maths Exercise 10.4 Problem 5**

## Draw a triangle ABC in which AB = 5 cm, BC = 6 cm and ∠ABC = 60º . Construct a triangle similar to ∆ ABC with scale factor 5/7. Justify the construction

**Summary:**

A triangle ABC with AB = 5 cm, BC = 6 cm and ∠ABC =60º is drawn. A triangle similar to ∆ ABC with scale factor 5/7 is constructed

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