# Draw a triangle ABC in which AB = 5 cm, BC = 6 cm and $ABC= 60^{\circ}$.Construct a triangle similar to ABC with scale factor $\frac{5}{7}$ . Justify the construction

Solution
Given : AB = 5 cm, BC = 6 cm

Steps of construction

1. Draw line segment AB = 5 cm
2. draw $< ABO= 60^{\circ}$  B taking as a centre draw an arc of radius BC=6cm
3. Join AC, DABC is the required triangle
4.  From point A draw any ray $A{A}'$   with acute angle $\angle BA{A}'$
5.  Mark 7 points $B_{1},B_{2},B_{3},B_{4},B_{5},B_{6},B_{7}$  with equal distance.
6. Join $B_{7}B$  and form $B_{5}$  draw $B_{5}X\parallel B_{7}B\, \, BY$making the angle equal From point X draw $XY\parallel BC$ intersecting AC at Y. Then, DAMN is the required triangle whose sides are equal to $\frac{5}{7}$  of the corresponding sides of the $\bigtriangleup ABC$..

Justification: Here, $B_{5X}\parallel B_{7}B$  [by construction]
$\therefore \frac{AX}{XB}= \frac{5}{2}\Rightarrow \frac{XB}{AX}= \frac{2}{5}$
Now $\frac{AB}{AX}= \frac{AX+XB}{AX}$
$1+\frac{XB}{AX}= 1+\frac{2}{5}= \frac{7}{5}$
Also, $XY\parallel BC$
$\therefore \bigtriangleup AXY\sim \bigtriangleup ABC$
$\frac{AX}{AB}= \frac{AY}{AC}= \frac{YX}{BC}= \frac{5}{7}$

## Most Viewed Questions

### Preparation Products

##### Knockout NEET 2024

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 40000/-
##### Knockout NEET 2025

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 45000/-
##### NEET Foundation + Knockout NEET 2024

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 54999/- ₹ 42499/-
##### NEET Foundation + Knockout NEET 2024 (Easy Installment)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 3999/-
##### NEET Foundation + Knockout NEET 2025 (Easy Installment)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 3999/-
Boost your Preparation for JEE Main with our Foundation Course

Exams
Articles
Questions