NCERT solution Class 9 constructions

NCERT Solutions

Class 9 Maths

Constructions

NCERT Questions

Ex.11.1 Q.1
Ex.11.1 Q.2
Ex.11.1 Q.3
Ex.11.1 Q.4
Ex.11.1 Q.5
Ex.11.1 Q.6
Ex.11.2 Q.2
Ex.11.2 Q.3
Ex.11.2 Q.4
Ex.11.2 Q.5

Ex.11.1 Q.5

Construct an equilateral triangle, given its side and justify the construction.

Let us draw an equilateral triangle of side 5 cm. We know that all sides of an equilateral triangle are equal.

Therefore, all sides of the equilateral triangle will be 5 cm. We also know that each angle of an equilateral triangle is 60⁰.

The below given steps will be followed to draw an equilateral triangle of 5 cm side.

Step I: Draw a line segment AB of 5 cm length. Draw an arc of some radius, while taking A as its

centre. Let it intersect AB at P.

Step II: Taking P as centre, draw an arc to intersect the previous arc at E. Join AE.

Step III: Taking A as centre, draw an arc of 5 cm radius, which intersects

extended line segment AE at C. Join AC and BC.

∆ABC is the required equilateral triangle of side 5 cm.

Justification of Construction:

We can justify the construction by showing ABC as an equilateral triangle i.e.,

AB = BC = AC = 5 cm and ∠A = ∠B = ∠C = 60⁰.

In ∆ABC, we have AC = AB = 5 cm and ∠A = 60⁰.

Since AC = AB, ∠B = ∠C

[Angles opposite to equal sides of a triangle]

In ∆ABC,

∠A + ∠B + ∠C = 180°

[Angle sum property of a triangle]

∠ 60⁰ + ∠C + ∠C = 180⁰

∠ 60⁰ + 2 ∠C = 180⁰

2 ∠C = 180⁰ − 60⁰ = 120⁰

∠C = 120⁰/2

∠C = 60⁰

∠B = ∠C = 60⁰

We have, ∠A = ∠B = ∠C = 60⁰ …………......(1)

So, ∠A = ∠B and ∠A = ∠C

BC = AC and BC = AB

[Sides opposite to equal angles of a triangle]

∠ AB = BC = AC = 5 cm ..........................(2)

From equations 1 and 2, ∆ABC is an equilateral triangle.

Video solution:

Constructions Class 9 Maths NCERT Chapter 11 NCERT Solutions

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NCERT solutions of Constructions Class 9 Maths - all questions of all exercises are solved. Q. No. 1, 2, 3, and so on. Complete explanation and detailed solution makes them the best videos for Class 9 Maths Constructions NCERT solutions.