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.
Draw the triangle with the given conditions.
Two triangles are said to be similar if their corresponding angles are equal, are said to satisfy Angle-Angle-Angle (AAA) Axiom.
Steps of constructions:
- Draw a line BC = 6 cm.
- At B, make ∠C = 60° and cut an arc at A on the same line so that BA = 5 cm. Join AC, ΔABC is obtained.
- Draw the ray BX such that ∠CBX is acute.
- Mark 4 (since 4 > in 3/4) points B₁, B₂, B₃, B₄ on BX such that BB₁ = B₁B₂ = B₂B₃ = B₃B₄
- Join B₄ to C and draw B₃C' parallel to B₄C 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
In ΔBB₄C , B₃C' || B₄C
Hence by Basic proportionality theorem,
B₃B₄/BB₃ = 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
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
A triangle ABC of sides 6cm, 5 cm and ∠ABC = 60° and another triangle A'BC' of sides 3/4 of the corresponding sides of triangle ABC have been constructed.
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