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.7

Draw a right triangle in which the sides (other than hypotenuse) are of lengths 4 cm and 3 cm.

the construct another triangle whose sides are times the corresponding sides of the given triangle.

Give the justification of the construction.

It is given that sides other than hypotenuse are of lengths 4 cm and 3 cm.

Clearly, these will be perpendicular to each other. The required triangle can be drawn as follows:

Step 1. Draw a line segment AB = 4 cm. Draw a ray SA making 90⁰ with it.

Step 2. Draw an arc of 3 cm radius while taking A as its centre to intersect SA at C.

Join BC. So, ∆ABC is the required triangle.

Step 3. Draw a ray AX making an acute angle with AB, opposite to vertex C.

Step 4. Locate 5 points (as 5 is greater in 5 and 3), A₁, A₂, A₃, A₄, A₅,

on line segment AX such that: AA₁ = A₁ A₂ = A₂ A₃ = A₃ A₄ = A₄ A₅.

Step 5. Join A₃ B. Draw a line through A₅ parallel to A₃ B intersecting extended line segment AB at B'.

Step 6. Through B', draw a line parallel to BC intersecting extended line segment AC at C'.

So, ∆AB'C' is the required triangle.

Justification:

The construction can be justified by proving that

AB’ = AB, B’C’ = BC, AC’ = AC

In ∆ABC and ∆AB'C',

∠ABC = ∠AB'C'

(Corresponding angles)

∠BAC = ∠B'AC'

(Common)

So, ∆ABC ∼ ∆AB'C'

(AA similarity criterion)

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

In ∆AA₃B and ∆AA₅B',

∠A₃AB = ∠A₅AB'

(Common)

∠AA₃ B = ∠AA₅ B'

(Corresponding angles)

So, ∆AA₃B ∼ ∆AA₅B'

(AA similarity criterion)

=> AB ÷ AB’ = AA₃ ÷ AA₅

=> AB ÷ AB’ = ………... (2)

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

AB ÷ AB’ = BC ÷ B’C’ = AC ÷ AC’ =

AB’ = AB, B’C’ = BC, AC’ = 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.