A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.

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 A1, A2, A3, A4, A5, A6 and A7 on AX where AA1 = A1A2 = A2A3 = A3A4 = A4A5 = A5A6 = A6A7

7. Join A7B and from the point A5 construct A5M||A7B 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.

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

Justification:

Consider AA1 = A1A2 = A2A3 = A3A4 = A4A5 = A5A6 = A6A7 = x

From the construction

A5M || A7B

AM/MB = AA5/A5A7 = 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

☛ Related Questions:

Math worksheets and
visual curriculum