# CBSE Important Questions Class 6 Maths Chapter 14

## Important Questions Class 6 Maths Chapter 14 – Practical Geometry

Maths is an important subject that students study in school. The last chapter of Class 6 Maths is about different geometric instruments and the construction of different geometric shapes.

Students will learn about geometric instruments such as scales, protectors, compasses etc. These instruments are simple instruments that help to draw different geometric shapes, and they will also learn how to draw circles, line segments, and angles with those instruments. They must practice questions from this chapter to score better in exams.

The experts of Extramarks have made the Important Questions Class 6 Maths Chapter 14 to help students practice. They have collected the questions from different sources such as the CBSE sample papers, CBSE past years’ question papers and important reference books. Thus, it will help students to solve different questions and improve their concepts.

Extramarks is a leading company that provides a wide range of study materials to students, and you may register on the official website of Extramarks and download these materials. You will find the CBSE syllabus, BCSE extra questions, CBSE past years’ question papers, CBSE revision notes, NCERT books, NCERT exemplars, NCERT solutions, important questions, vital formulas and many more.

## Get Access to CBSE Class 6 Maths Important Questions with Solutions

Also, get access to CBSE Class 6 Maths Important Questions for other chapters too:

 CBSE Important Questions for Class 6 Maths Sr No Chapter No Chapter Name 1 Chapter 1 Knowing Our Numbers 2 Chapter 2 Whole Numbers 3 Chapter 3 Playing with Numbers 4 Chapter 4 Basic Geometrical Ideas 5 Chapter 5 Understanding Elementary Shapes 6 Chapter 6 Integers 7 Chapter 7 Fractions 8 Chapter 8 Decimals 9 Chapter 9 Data Handling 10 Chapter 10 Mensuration 11 Chapter 11 Algebra 12 Chapter 12 Ratio and Proportion 13 Chapter 13 Symmetry 14 Chapter 14 Practical Geometry

## Important Questions Class 6 Maths Chapter 14 – With Solutions

The experts of Extramarks have made this question series so that students can solve questions regularly. They have collated these questions from several sources such as the textbook exercises, CBSE sample papers, CBSE past years’ question papers and important reference books. They have solved these questions too. Thus, the Important Questions Class 6 Maths Chapter 14 will help students to score better in exams. The important questions are-

Question 1. Construct, with the help of a ruler and compasses, the angles of the following measures:

(i) 60°

(ii) 30°

(iii) 90°

(iv) 120°

(v) 45°

(vi) 135°

(i) 60 degree

The following steps should be followed to construct an angle of 60 degrees.

(a) Firstly, Draw a line l and then mark a point P on it. Then take point P as a centre, and with the convenient radius, then draw an arc of a circle such that it intersects the line l at point Q.

(b) Now, Take Q as the centre point and with the same radius as before, then draw an arc intersecting the previously drawn arc, and name it point R.

(c) Join the points and form PR. PR is the required ray that makes 60 with line l.

(ii) 30 degrees

The following steps should be followed to construct an angle of 30 degrees.

(a) Draw a line l and mark a point P on the line. Now By taking point P as the centre point and with the convenient radius, draw an arc of a circle such that it intersects the line l at point Q.

(b) Now, Take point Q as the centre point and with the same radius as before, draw an arc which intersects the previously drawn arc at point R.

(c) Now, By taking the points Q and R as the centres and with a radius of more than the 1 / 2 RQ, draw the arcs such that they can intersect each other at point S. Join these ray PS, which is the required ray making 30 degrees with the line l.

(iii) 90 degree

The following steps should be followed to construct an angle of measure 90 degrees.

(a) Draw a line l and mark a point P on the line. Then take point P as the centre, and with the convenient radius, also draw an arc of a circle such that it intersects at line l at point Q.

(b) Now Take the point Q as the centre, and with the same radius as before, draw an arc that intersects the previously drawn arc at the point R

(c) By taking the point R as a centre and with the help of the same radius as before, draw an arc intersecting the arc at S as shown in the given figure

(d) Now take the points R and S as the centre, and draw an arc of the same radius that intersects each other at point T.

(e) Join and form PT, which is the required ray making 90 degrees with the line l.

(iv) 120 degrees

The following steps should be followed to construct an angle of measure 120 degrees.

(a) Draw a line l and mark a point P on it. Then taking point P as a centre and with the convenient radius, then draw an arc of a circle such that it intersects the line l at point Q.

(b) By taking point Q as the centre point and with the same radius taken as before, draw an arc which intersects the previously drawn arc at point R.

(c) Take the point R as the centre point and with the same radius taken as before, draw an arc such that it intersects the arc at point S, as shown in the given figure.

(d) Join the point PS, which is the required ray making 120 degrees with the line l

(v) 45 degrees

The following steps should be followed to construct an angle of measure 45 degrees.

(a) Draw a line l and mark a point P on it. Then take point P as a centre, and with the convenient radius, now draw an arc of a circle such that it intersects the line l at point Q.

(b) Take the point Q as a centre and with the same radius taken as before, draw an arc intersecting the previously drawn arc at the point R

(c) By taking point R as a centre and with the same radius taken as before, draw an arc such that it intersects the arc at point S, as shown in the given figure.

(d) Take the points R and S as centres and draw the arcs of the same radius such that they intersect each other at point T

(e) Join the points and form PT. Let this intersect the major arc at point U.

(f) Now take the points Q and U as centres and draw arcs with a radius of more than 1 / 2 QU to intersect each other at point V. Then Join PV.

PV is the required ray making 45 degrees with the line.

(vi) 135 degrees

The following steps should be followed to construct an angle of measure 135 degrees.

(i) Draw a line as l and mark a point P on it. Then taking P as the centre and with a convenient radius, draw a semicircle which then intersects the line l at points Q and R, respectively.

(ii) By taking the point R as the centre and with the same radius as before, draw an arc which intersects the previously drawn arc at point S

(iii) Taking the point S as the centre point and with the same radius as before, draw an arc so that it intersects the arc at point T, as shown in the given figure

(iv) Now, Take the points S and T as the centre point, then draw arcs of the same radius to intersect each other at point U.

(v) Join the points to form PU. Let this intersect the arc at point V. Now take the points Q and V as the centres, and with a radius of more than 1 / 2 QV, draw arcs to intersect each other at point W.

(vi) Join the pints to form PW, which is the required ray making 1350 with the line l

Question 2. Draw an angle of 70 degrees. Make a copy of it with the help of only a straight edge and compasses.

The following steps should be followed to construct an angle of measure 70degree with its copy.

(i) Draw a line and name it l, and then mark a point O on it. Now place the centre of the protractor at point O and the zero edge along line l.

(ii) Mark point A at an angle to measure 70 degrees. Join both points to form OA. Now OA is the ray making 70 degrees with the line l. With point O as the centre, draw an arc of a convenient radius in the interior at a 70-degree angle. Let this intersect both rays of angle 70 at points B and C, respectively

(iii) Draw a line as M and mark a point P on the line. Again draw an arc with the same radius as before, with P as the centre. Let it cut the line m at point D

(iv) Now, Adjust the compasses up to the length of BC. With this radius, draw an arc taking point D as the centre, which then intersects the previously drawn arc at point E.

(v) Join these points to form PE. Here the PE is the required ray which makes the same angle of measuring 70 degrees with the line m

Question 3. Draw an angle of 40 degrees. Also, Copy its supplementary angle.

The following steps should be followed to construct an angle of measure 45 degrees and a copy of its supplementary angle.

(i) Draw a line segment and then mark a point O on the line segment. Place the centre of the protractor at point O and the zero edge along the line segment.

(ii) Mark a point as A at an angle of measure 40 degrees. Join these points to form OA. Here OA is the required ray making 40 degrees with ∠POA, is the supplementary angle of 400

(iii) With point O as the centre point, draw an arc of the convenient radius in the interior of the angle ∠POA. Let this intersects both rays of ∠POA at points B and C, respectively.

(iv) Now Draw a line m and mark a point S on the line. Again draw an arc by taking point S as a centre with the same radius that is used before. Let it cut the line m at point T.

(v) Now adjust the compasses up to the length of ray BC. Taking point T as a centre, draw an arc with this radius which will then intersect the previously drawn arc at point R.

(vi) Join the ray RS. Here that RS is the required ray which makes the same angle with the line m, as they are supplementary of 400 [which is 140 degrees]

Now Draw a line l and a point X on it. Through X, draw a line segment XY¯¯¯¯¯¯¯¯ perpendicular to the line l. Now draw a perpendicular to the ray XY at Y. (use ruler and compasses)

Solution :

Step 1. Given a point X on a line, l.

Step 2. With X as a centre and a convenient radius, construct a part circle (arc) intersecting line l at two points, A and B.

Step 3. With these points A and B as centres and a radius greater than AX, construct two arcs which cut each other at Y.

### Benefits of Solving Important Questions Class 6 Maths Chapter 14

Practice is very important for students. It helps them in various ways and improves their preparation for exams. It helps them to clear their concepts, generate interest in the subject matter and boost confidence for the exams. The experts of Extramarks have made the question series to help students to practice regularly. They have taken help from different sources. The Important Questions Class 6 Maths Chapter 14 will help students in various ways. The benefits are-

• The experts have collected the questions from various sources. They have accumulated the questions from the textbook exercises, CBSE sample papers, NCERT exemplars and important reference books. They have also included a few questions from the CBSE past years’ question papers so that students may have an idea about which type of questions come in exams. So, students don’t have to search for questions in different books, but they will find them in the Class 6 Maths Chapter 14 Important Questions. Finding questions in different books will be tough for the students, but the experts have included those questions in this pdf. So, the question series will help them build practice habits.
• The experts have solved the questions. They have given a step-by-step solution process so students can understand it easily. Experienced professionals have further checked the answers to ensure the best quality of the content. So, students can take help from the Maths Class 6 Chapter 14 Important Questions if they need help solving them. They can also check their answers with the experts’ answers. Thus, it will help them to solve the questions and clear their doubts. It will boost their confidence.
• Practice is very important in Mathematics. They should solve questions as much as possible to strengthen their bases on the subject. Often, students need more than textbook exercises and should take help from other sources. Keeping this fact in mind, the experts of Extramarks have made the Chapter 14 Class 6 Maths Important Questions. They collected the questions from different sources and solved them. So, it will help the students to upgrade their preparation for exams and score better.

You may have heard about Extramarks. We provide all the study materials related to CBSE and NCERT. You may register on our official website and download the study materials. We provide CBSE syllabus, CBSE past years’ question papers, CBSE sample papers, CBSE revision notes, CBSE extra questions, NCERT exemplar, NCERT solutions, NCERT important questions, NCERT books, vital formulas and many more. Like the Important Questions Class 6 Maths Chapter 14, you will also find important questions for other chapters. Links to the study materials are given below-

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Q.1 Which of the following figures shows the bisection of angle 60° and 30° to construct an angle of measure 15°?    Marks:1

Ans To draw an angle of 15°, first draw an angle of 60°. Then bisect it and draw an angle of 30°. Again bisecting the angle of 30°, we get an angle of 15°.

Q.2

Which of the following diagram shows the correct construction of an angle of 75°? (i) (ii) (iii)

(i) only

Both (ii) and (iii)

(ii) only

Both (i) and (ii)

(i) only

Both (ii) and (iii)

(ii) only

Both (i) and (ii)

Marks:1

Ans

Figure (ii) shows the correct construction of a 75° angle.
To construct an angle of 75° , first, construct an angle of 60° and then 90°
Then, bisect the angle formed between these two angles to construct an angle of 75°

Q.3 Construct

of length 7.9 cm. From this, cut off

of length 3.6 cm. Measure

$\overline{)\mathrm{BC}}$

.

Step 1: With the help of a ruler, draw a line segment AB of length 7.9 cm. Step 2: Using compasses find a point C on the line segment AB so that line segment AC = 3.6 cm. Step 3: Now measure line segment BC. We find that
Marks:3

Ans

Step 1: With the help of a ruler, draw a line segment AB of length 7.9 cm. Step 2: Using compasses find a point C on the line segment AB so that line segment AC = 3.6 cm. Step 3: Now measure line segment BC. We find that

$\overline{)\mathrm{BC}}$

= (7.9 3.6) = 4.3 cm.

Q.4 Draw two circles of equal radii with centres A and B such that each one passes through the centre of the other.Let them intersect at C and D. Check whether

and

are at right angles or not.

The required figure is shown below.
On examining the figure, we find that the line segments meet at right angle. Marks:1

Ans

The required figure is shown below.
On examining the figure, we find that the line segments meet at right angle. Q.5 How many circles, you can draw, passing through a given point ?

Marks:1

Ans

Infinite number of circles can be drawn passing through a given point.