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RS Aggarwal Class 7 Solutions Chapter-17 Constructions

Q: 1. What are some of the properties of Triangles?

Some of the general properties of all triangles are:The sum of all the three angles of a triangle is equal to 180 degrees.The exterior angle of a triangle is equal to the sum of interior angles that are opposite to the given exterior angle. So, in a triangle ABC, the exterior angle A = ∠ABC + ∠BCA.If you add any two sides of a triangle, it is always greater than the measure of the 3rd side of the triangle.In a right-angled triangle, the hypotenuse square (the side opposite to the right-angle) is equal to the sum of squares of the other two sides. So in a triangle ABC which is right-angled at C, AB2 = AC2 + CB2. This is the Pythagoras theorem.

Q: 3. What are the various measurements required to construct a triangle?

A triangle can be drawn if:All its 3 sides are given - SSS criterionTwo sides and the angle included between the sides is known - SAS criterionTwo angles and the side common to the angles is given - ASA criterionWe know the hypotenuse (the side opposite to 90 degrees) and one of the sides - RHS criterion for a right-angled triangle.

Q: 4. Is it important to write steps in Construction Chapters?

Yes, it is crucial for the following reasons:It provides the idea to the teacher that you are familiar with all of the steps and have completed them appropriately.It accomotes for the mark allotted to the question with giving supplementary information.If you did not write steps but completed the building correctly, you may lose points for failing to do so.If your final structure is incorrect but you completed half of it correctly, the steps of building are proof of that, and you may receive some marks for the answer (depending on teacher)

RS Aggarwal Solutions

RS Aggarwal Class 7 Solutions Chapter-17 Constructions

Class 7 RS Aggarwal Chapter-17 Constructions Solutions - Free PDF Download

For students looking for simple and accurate solutions in Maths, the RS Aggarwal Class 7 Maths Chapter 17 solutions designed by expert teachers of Vedantu is one of the most reliable online resources. Our team has experienced mathematicians who cater to students' needs and give easily comprehensible solutions that students can grasp fast. The RS Aggarwal Solutions Class 7 Chapter 17 deals with practical geometry and constructions, where students learn how to draw different kinds of lines (parallel, perpendicular, angles, etc.) and triangles. If you get the basics of this topic right, it will help you immensely in solving more complicated topics later in your academic life. That is why it becomes essential to seek help from professionals like the RS Aggarwal Solutions Class 7 ch 17 from Vedantu.

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Download NCERT Solutions for Class 7 Maths Chapter 17 Constructions PDF

Having solutions in a PDF format is a great way to revise formulas and difficult sums quickly. Vedantu has readily made available the RS Aggarwal Class 7 Construction in PDF format on their official website. Students can download the solutions for RS Aggarwal Class 7 Maths ch 17 PDF on their devices so that they do not need an internet connection whenever they want to refer to it.

Construction in Maths for Class 7

The Construction Class 7 RS Aggarwal builds on your previous knowledge of shapes and how to draw them. This chapter will learn how to draw a line segment of a specific length, a line perpendicular to another line, parallel lines, and different kinds of triangles. The main takeaways of this chapter are:

Line Segment - When you take two points on a line, then the part within those two points is called a line segment.
A Line Perpendicular to A Line Segment - Any line which intersects a line segment at a point and makes 90 degrees is called a line perpendicular to the other line segment.
Constructing a line that is parallel to another line segment through a point that is not on the line:

We will use a ruler and compass only to construct this line.
Draw a line AB and take C as a point that is outside of it.
Now take a point D on the line AB and join it with C.
Keeping D as the center, use a compass to draw an arc of any radius cutting AB at E and DC at F.
Now take C as the center and draw another arc with the same radius as the one you used to draw the above arc.
Measure line EF with the compass and mark an arc of the same measurement from C to cut the arc at S.
When you join CS, it will give you a parallel line to the line segment AC.

Constructing a triangle with SSS (all 3 sides are known) criterion

Let us say we have to draw a triangle PQR with PQ = 6 cm, QR = 5 cm, and PR = 9 cm

Draw a rough sketch of the triangle first with the given measurements.
Draw a line segment PQ
Since PR = 9 cms, take P as the center and draw an arc of 9 cms.
Now QR = 5 cms so take Q as the center and draw an arc of 5 cms in such a way that it intersects the arc drawn in the previous step.
The point of intersection of both the arcs is the point R.
Join PR and QR to get the required triangle PQR.

Constructing a triangle with SAS (two sides and the included angle is given) criterion

Let us say that the triangle ABC we need to draw has two sides AB = 8 cm, AC = 5 cms, and ∠CAB = 60 degrees.

First, draw a rough sketch of the triangle based on the information given.
Draw a line segment AB = 8 cms.
Now draw a line AX which makes an angle of 60 degrees at A, the line AC will lie somewhere on this ray of the angle.
Now AC = 5 cms so with A as center draw an arc of 5 cms on AX that is the point C
Now join BC to get the required triangle.

Exercises

17 A - 3 long type questions based on constructing various kinds of line segments.
17 B - 13 long type questions based on constructing triangles on different criteria.
17 C - 38 questions which are a mix of short and long type answers. They are based on different types of angles and triangles.
Test paper - 18 questions

All the Exercise questions with solutions in Chapter-17 Constructions are given below:

Exercise (Ex 17A) 17.1

Exercise (Ex 17B) 17.2

Exercise (Ex 17C) 17.3

Preparation Tips for RS Aggarwal Class 7 Maths Chapter 17

Maths is a hands-on subject, and particularly geometry and constructions can only be learned by practicing as many different kinds of problems as possible.
Try to pick out sums from RS Aggarwal Class 7 Maths Chapter 17 which you find difficult and hone your skills in those kinds of problems.
Always draw a rough sketch of whatever diagram is presented in the RS Aggarwal Solutions Class 7 ch 17 to get an idea of what is being asked.
Remember all the criteria for triangles (SSS, SAS, RHS, etc.) and write them down in a note to stick it in your room. This way, you can remember them all quickly.

FAQs on RS Aggarwal Class 7 Solutions Chapter-17 Constructions

1. What are some of the properties of Triangles?

Some of the general properties of all triangles are:

The sum of all the three angles of a triangle is equal to 180 degrees.
The exterior angle of a triangle is equal to the sum of interior angles that are opposite to the given exterior angle. So, in a triangle ABC, the exterior angle A = ∠ABC + ∠BCA.
If you add any two sides of a triangle, it is always greater than the measure of the 3rd side of the triangle.
In a right-angled triangle, the hypotenuse square (the side opposite to the right-angle) is equal to the sum of squares of the other two sides. So in a triangle ABC which is right-angled at C, AB² = AC² + CB². This is the Pythagoras theorem.

2. How will you construct a right-angle triangle if you are given the measure of its hypotenuse (7 cms) and one more side (AB = 4.5 cms)?

First, draw a rough sketch of a triangle ABC which is right-angled at A and has hypotenuse equal to 7 cm and another side as 4.5 cm.

Draw a line segment AB = 4.5 cms.
Draw a line AS which is perpendicular to point A, the point C would lie somewhere on this perpendicular line.
With B as the center, draw an arc of length 7 cms which intersects the line AS at C.
Join BC, and you get the required right-angles triangle ABC.

3. What are the various measurements required to construct a triangle?

A triangle can be drawn if:

All its 3 sides are given - SSS criterion
Two sides and the angle included between the sides is known - SAS criterion
Two angles and the side common to the angles is given - ASA criterion
We know the hypotenuse (the side opposite to 90 degrees) and one of the sides - RHS criterion for a right-angled triangle.

4. Is it important to write steps in Construction Chapters?

Yes, it is crucial for the following reasons:

It provides the idea to the teacher that you are familiar with all of the steps and have completed them appropriately.
It accomotes for the mark allotted to the question with giving supplementary information.
If you did not write steps but completed the building correctly, you may lose points for failing to do so.
If your final structure is incorrect but you completed half of it correctly, the steps of building are proof of that, and you may receive some marks for the answer (depending on teacher)

5. How do we use Geometry in everyday life ?

The best use of geometry in everyday life is in the construction of buildings, dams, rivers, highways, temples, and other structures. Geometrical concepts are used to create smartphones, laptops, computers, and other electronic devices. In fact, the games we play also employ geometry to determine the relationship between distance and the shapes of planned objects.