NCERT solution Class 10 constructions

NCERT Solutions

Class 10 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.11.1 Q.7
Ex.11.2 Q.1
Ex.11.2 Q.2
Ex.11.2 Q.3
Ex.11.2 Q.4
Ex.11.2 Q.5
Ex.11.2 Q.6
Ex.11.2 Q.7

Ex.11.1 Q.6

Draw a triangle ABC with side BC = 7 cm, ∠B = 45⁰, ∠A = 105⁰.

Then, construct a triangle whose sides are times the corresponding side of ∆ABC.

Give the justification of the construction.

Given, ∠B = 45⁰, ∠A = 105⁰

Sum of all interior angles in a triangle is 180⁰.

∠A + ∠B + ∠C = 180⁰

=> 105⁰ + 45⁰ + ∠C = 180⁰

=> ∠C = 180⁰ − 150⁰

=> ∠C = 30⁰

The required triangle can be drawn as follows:

Step 1. Draw a ∆ABC with side BC = 7 cm, ∠B = 45⁰, ∠C = 30⁰.

Step 2. Draw a ray BX making an acute angle with BC on the opposite side of vertex A.

Step 3. Locate 4 points (as 4 is greater in 4 and 3), B₁, B₂, B₃, B₄, on BX.

Step 4. Join B₃ C. Draw a line through B4 parallel to B₃ C intersecting extended BC at C'.

Step 5. Through C', draw a line parallel to AC intersecting extended line segment at C'.

Now, ∆A'BC' is the required triangle.

Justification:

The construction can be justified by proving that

A’B = AB, BC’ = BC, A’C’ = AC

In ∆ABC and ∆A'BC',

∠ABC = ∠A'BC' (Common)

∠ACB = ∠A'C'B (Corresponding angles)

So, ∆ABC ∼ ∆A'BC' (AA similarity criterion)

AB ÷ A’B = BC ÷ BC’ = AC ÷ A’C’ ……... (1)

In ∆BB₃C and ∆BB₄C',

∠B₃BC = ∠B₄BC'

(Common)

∠BB₃C = ∠BB₄C'

(Corresponding angles)

So, ∆BB₃ C ∼ ∆BB₄ C'

(AA similarity criterion)

BC ÷ BC’ = BB₃ ÷ BB₄

=> BC ÷ BC’ = …………. (2)

On comparing equations (1) and (2), we obtain

=> AB ÷ A’B = BC ÷ BC’ = AC ÷ A’C’ =

=> A’B = AB, BC’ = BC, A’C’ = AC

This justifies the construction.

Video solution:

Constructions Class 10 Maths NCERT Chapter 11 NCERT Solutions

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NCERT solutions of Constructions Class 10 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 10 Maths Constructions NCERT solutions.