Constructions Class-7 RS Aggarwal ICSE Maths Goyal Brothers

Constructions Class-7 RS Aggarwal ICSE Maths Goyal Brothers Prakashan Chapter-22 Solutions. We provide step by step Solutions of Exercise / lesson-22 Properties of  Constructions for ICSE Class-7 RS Aggarwal Mathematics.

Our Solutions contain all type Questions with Exe-22 to develop skill and confidence. Visit official Website CISCE for detail information about ICSE Board Class-7 Mathematics.

Board	ICSE
Publications	Goyal brothers Prakshan
Subject	Maths
Class	7th
Chapter-22	Constructions
Writer	RS Aggrawal
Book Name	Foundation
Topics	Solution of Exe-22 to develop skill and confidence
Academic Session	2021-2022

Constructions Class-7 RS Aggarwal ICSE Maths Goyal Brothers Prakashan Chapter-22 Solutions

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Exe-22

Page 242-243

Question 1:

Draw a line segment AB = 5.2 cm. Draw a perpendicular to it from a point outside line AB by using.

(i) ruler and compasses

(ii) ruler and set squares.

Answer :

(i) 

Steps :

(a) Draw a line segment AB = 5.2 cm and a point P outside it.

(b) With centre P and with suitable radius draw an arc intersecting AB at C and D.

(c) With centre C and D, and radius equal to a bit more than half of CB, draw arcs intersecting each other at R.

(d) Join PR intersecting AB at Q. PQ is the required perpendicular.

(ii) 

Steps

(a) Draw a line segment AB = 5.2 cm and a point P outside of it.

(b) Place ruler along AB and place a set square so that one of its shorter edge touches the line AB

(c) Hold ruler formerly and move the set square along it until its other shorter edge just touches the point P.

(d) Draw a line PQ along this edge meeting at P then PQ is the required perpendicular.

Question 2:

Daw a line segment AB = 4.8 cm. Take a point P on it such that BP = 2.3 cm. Draw a perpendicular to AB at point P using.

(i) ruler and compasses

(ii) Using ruler and compasses.

Answer :

(i) 

Steps :

(a) Draw a line segment AB = 4.8 cm and take a point P on it such that BP = 2.3 cm

(b) With centre P and a suitable radius draw an arc meeting AB at E and F.

(c) With centres E and F, draw two arcs intersecting each other at C.

d) Join QCP

Then QP is perpendicular at AB.

(ii)

Steps :

(a) Draw a line segment AB = 4.8 cm and take a point P on it such that BP = 2.3 cm.

(b) Place ruler along the line AB and one shorter side along AB.

(c) Move the set square along the ruler such that the other shorter side just touches the point P on AB.

(d) Draw line PQ along the side of set square.

Then QP is the required perpendicular.

Question 3:

Draw any triangle ABC. Through A, draw a line parallel to BC using.

(i) ruler and compasses

(ii) using ruler and set square.

Answer :

(i) Using ruler and compasses :

Steps :

(a) Construct a A ABC with the given data

(b) With centre B and a suitable radius, draw an arc ER meeting BC at E and BA at E.

(c) With centre A draw an arc of the same radius meeting AB at G.

(d) Cut off A GH = EF.

(e) Join AH and produce it both sides, Then PQ || BC through A.

(ii) Using set square

Steps :

(a) Place set square along side BC of A ABC such that its one of the shorter side touches AB.

(b) Place ruler vertically along other shorter side of the set square.

(c) Now move the set square along the ruler until its horizontal edge touches the vertex A.

(d) Draw a straight line PQ along this edge of set square.

Then PQ is parallel to BC.

Question 4:

Construct a AABC such that :

(i) AB = 5 cm, BC = 46 cm and AC 43 cm.

(ii) BC = 6 cm, CA = 4 cm and AB = 35 cm

(iii) CA = 48 cm. CB = 42 cm and AB = 4.5 cm.

Answer :

(i)

Steps :

(a) Draw a line segment AB = 5 cm.

(b)  With A as centre and radius equal to 4.3 cm, draw an arc.

(c) With B as centre and radius equal to 4.6 cm, draw another arc cutting the previous arc at

(d) Join AC and BC.

So, ABC is the required triangle.

(ii) 

Steps :

(a) Draw a line segment BC = 6 cm.

(b) With B as centre draw an arc of 3.5 cm.

(c) With C as centre draw an arc ot 4 cm, which cuts the previous arc at A.

(d)  Join AB and AC.

:. △ ABC is the required triangle.

(iii) 

Steps :

(a) Draw line segment CA = 4.8 cm.

(b) With Cas centre draw an arc of 4.2 cm.

(c) With A centre draw an arc of 4.5 cm, which cuts the prev1ous arc at B.

(d) Join BC and AB.

△ ABC is the required triangle.

Question 5:

Construct a △ ABC such that:

(i) BC =5 cm, ∠BCA = 60° and CA = 4.3 cm

(ii) AB = 3.7 cm, ∠A = 45° and AC = 5.3cm

Answer :

(i) Steps :

(a)  Draw a line segment BC = 5 cm.

(b)  At B, construct ∠BCX = 60°

(c)  With C as centre cut CA = 4.3 cm from CX.

(d)  Join AB

△ ABC is the required triangle.

(ii) Steps :

(a) Draw a line segment AB = 3.7cm.

(b)  At A, draw a ray AX making an angle of 450 and cut off AC = 5.3 cm

(c) Join BC.

Then △ABC is the required triangle.

Question 6:

Construct a △XYZ, such that :

(i) XY= 45° cm, ∠X = 60° and ∠Y – 45°

(ii) YZ = 5 cm, ∠ZYX = 30° and ∠YZK = 75°

Answer :

(i) Steps :

(a)  Draw a line segment XY = 4.5 cm.

(b)  At X, construct ∠YXP = 60°

(c)  AL Y, construct ∠XYQ = 45°

(d) Let XP and YQ interest each other at

So, △XYZ s the required triangle.

(ii) Steps :

(a)  Draw a line segment YZ= 5 cm.

(b) At Y, construct ∠ZYP = 30°.

(c)  At Z, construct ∠YZQ = 75°

(d)  Let YP and ZQ intersect each other at X

△XYZ is the required triangle.

Question 7:

Construct an isosceles △ABC such that:

(i) base AB = 4.2 cm, base angle = 30°

(ii) base AC = 4.5 cm, base angle = 75°.

Answer :

(i) Steps :

(a)  Draw a line segment AB = 4.2 cm.

(b)  At A, construct ∠BAX = 30°.

(c)  At B, construct ∠ABY = 30°.

(d)  Let AX and BY intersect each other at C.

△ABC is the required triangle.

(ii) Steps :

(a) Draw a line segment AC = 4.5 cm.

(b) At A, construct ∠CAY = 75°

(c) At C, construct ∠ACY = 75°

(d) Let AX and CY intersect each other at B

△ABC 1s the required triangle.

Question 8:

Construct an isosceles △ABC such that AB = AC = 5 cm and  ∠A = 60°.

Answer :

Steps :

(a) Draw a line segment AB = 5 cm.

(b) At A, construct ∠BAX = 60°

(c) With A as centre cut AC = 5 Cm form AX.

(d)  Join BC.

△ABC is the required triangle.

Question 9:

Construct an isosceles △ ABC such

that AB = BC = 5.4 cm and ∠B = 30°

Answer :

Steps :

(a) Draw a line segment AB = 5.4cm

(b) At A, draw a ray AX making an angle of 60° and cut off AC = 5 cm

(c) Join BC.

Then △ ABC 18 the required triangle.

Question 10:

Construct an equilateral △ ABC in which BC = 5 cm.

Answer :

Steps :

(a) Draw a line segment BC = 5cm.

(b)  With centres B and C and radius 5 cm, draw two arcs intersecting each other at A.

(c)  Join AB and AC.

Then △ ABC is the required triangle.

Question 11:

Construct an equilateral △ ABC such that AB = 4.2cm.

Answer :

Steps :

(a) Draw line segment AB = 4.2 cm.

(b) With centres A and B and radius 4.2 cm, draw two arcs intersecting each other at C.

(c) Join AC and BC

Then △ ABC is the required triangle.

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Conditions necessary to construct a triangle

A triangle is a three-sided polygon. It has three sides, three vertices and three angles. We know that a unique triangle can be constructed if
(i) all three sides are given
(ii) two sides and included angle are given
(iii) two angles and the included side is given
(iv) the measure of the hypotenuse and a side is given in the right triangle.

Trick to construct a triangle

• Read basic concept of constructions
• Solve examples of your text book with geometry box
• draw a rough diagram
• write measurement value of side / angle on rough diagram
• known length side should be base rough diagram
• now draw base line of given length as real diagram
• draw other sides or angles as given conditions on real diagram
• write measurement value on real diagram

 –: End of Constructions Class-7 RS Aggarwal Solutions :–

Return to- RS Aggarwal Solutions for ICSE Class-7 Goyal Brothers Prakashan

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