Draw a triangle ABC with side BC = 6 cm, AB = 5 cm and ∠ABC = 60°. Then construct a triangle whose sides are 3/4 of the corresponding sides of the triangle ABC
Solution:

Draw the triangle with the given conditions.

Then draw another line that makes an acute angle with the baseline. Divide the line into m + n parts where m and n are the ratios given.

Two triangles are said to be similar if their corresponding angles are equal, are said to satisfy AngleAngleAngle (AAA) Axiom.

The basic proportionality theorem states that “If a straight line is drawn parallel to a side of a triangle, then it divides the other two sides proportionally".
Steps of constructions:
 Draw BC = 6 and
 At B, make ∠CBY= 60° and cut an arc at A so that BA = 5 cm. Join AC, ΔABC is obtained.
 Draw the ray BX such that ∠CBX is acute.
 Mark 4 (4 > in 3/4) points B_{1}, B_{2}, B_{3}, B_{4} on BX such that BB_{1} = B_{1}B_{2} = B_{2}B_{3} = B_{3}B_{4}
 Join B_{4} to C and draw B_{3}C' parallel to B_{4}C to intersect BC at C'.
 Draw C'A' parallel to CA to intersect BA at A’.
Now, ΔA'BC' is the required triangle similar to ΔABC where BA'/BA = BC'/BC = C'A'/CA = 3/4
Proof:
In ΔBB_{4}C' , B_{3}C'  B_{4}C
Hence by Basic proportionality theorem,
B_{3}B_{4}/BB_{3} = C'C/BC' = 1/3
C'C /BC' + 1 = 1/3 + 1
(C'C + BC')/BC' = 4/3
BC/BC' = 4/3 or BC'/BC = 3/4
Consider ΔBA'C' and ΔBAC
∠A'BC' = ∠ABC = 60°
∠BCA' = ∠BCA (Corresponding angles ∵ C'A'CA)
∠BA'C' = ∠BAC (Corresponding angles)
By AAA axiom, ΔBA'C' ~ ΔBAC
Therefore, corresponding sides are proportional,
BC'/BC = BA'/BA = C'A'/CA = 3/4
Video Solution:
Draw a triangle ABC with side BC = 6 cm, AB = 5 cm and ∠ABC = 60°. Then construct a triangle whose sides are 3/4 of the corresponding sides of the triangle ABC
NCERT Solutions Class 10 Maths  Chapter 11 Exercise 11.1 Question 5:
Draw a triangle ABC with side BC = 6 cm, AB = 5 cm and ∠ABC = 60°. Then construct a triangle whose sides are 3/4 of the corresponding sides of the triangle ABC
A triangle ABC of sides 6cm, 5 cm and ∠ABC = 60° and another triangle A'BC' of sides 3/4 of the corresponding ones of triangle ABC have been constructed.