NCERT solutions for Mathematics [English] Class 6 chapter 5 - Understanding Elementary Shapes [Latest edition]

What is the disadvantage of comparing line segments by mere observation?

Why is it better to use a divider than a ruler, while measuring the length of a line segment?

Draw any line segment, say `overline"AB"`. Take any point C lying in between A and B. Measure the lengths of AB, BC, and AC. Is AB = AC + CB?

[Note: If A, B, and C are any three points on a line such that AC + CB = AB, then we can be sure that C lies between A and B.]

If A, B, and C are three points on a line such that AB = 5 cm, BC = 3 cm, and AC = 8 cm, which one of them lies between the other two?

Verify, whether D is the midpoint of `overline"AG"`.

If B is the midpoint of `overline"AC"` and C is the midpoint of `overline"BD"`, where A, B, C, and D lie on a straight line, say why AB = CD?

Draw five triangles and measure their sides. Check-in each case, if the sum of the lengths of any two sides is always less than the third side.

What fraction of a clockwise revolution does the hour hand of a clock turn though, when it goes from 3 to 9?

What fraction of a clockwise revolution does the hour hand of a clock turn though, when it goes from 4 to 7?

What fraction of a clockwise revolution does the hour hand of a clock turn though, when it goes from 7 to 10?

What fraction of a clockwise revolution does the hour hand of a clock turn though, when it goes from 12 to 9?

What fraction of a clockwise revolution does the hour hand of a clock turn though, when it goes from 1 to 10?

What fraction of a clockwise revolution does the hour hand of a clock turn though, when it goes from 6 to 3?

Where will the hand of a clock stop if it starts at 12 and makes `1/2` of a revolution, clockwise?

Where will the hand of a clock stop if it starts at 2 and makes `1/2` of a revolution, clockwise?

Where will the hand of a clock stop if it starts at 5 and makes `1/4` of a revolution, clockwise?

Where will the hand of a clock stop if it starts at 5 and makes `3/4` of a revolution, clockwise?

Which direction will you face if you start facing east and make `1/2` of a revolution clockwise?

Which direction will you face if you start facing east and make `1 1/2` of a revolution clockwise?

Which direction will you face if you start facing west and make `3/4` of a revolution anti-clockwise?

Which direction will you face if you start facing south and make one full revolution? (Should we specify clockwise or anti-clockwise for this last question? Why not?)

What part of a revolution have you turned through if you stand facing east and turn clockwise to face north?

What part of a revolution have you turned through if you stand facing south and turn clockwise to face east?

What part of a revolution have you turned through if you stand facing west and turn clockwise to face east?

Find the number of right angles turned through by the hour hand of a clock when it goes from 3 to 6.

Find the number of right angles turned through by the hour hand of a clock when it goes from 2 to 8.

Find the number of right angles turned through by the hour hand of a clock when it goes from 5 to 11.

Find the number of right angles turned through by the hour hand of a clock when it goes from 10 to 1.

Find the number of right angles turned through by the hour hand of a clock when it goes from 12 to 9.

Find the number of right angles turned through by the hour hand of a clock when it goes from 12 to 6.

How many right angles do you make if you start facing south and turn clockwise to the west?

How many right angles do you make if you start facing north and turn anti-clockwise to the east?

How many right angles do you make if you start facing west and turn west?

How many right angles do you make if you start facing south and turn north?

Where will the hour hand of a clock stop if it starts from 6 and turns through 1 right angle?

Where will the hour hand of a clock stop if it starts from 8 and turns through 2 right angles?

Where will the hour hand of a clock stop if it starts from 10 and turns through 3 right angles?

Where will the hour hand of a clock stop if it starts from 7 and turns through 2 straight angles?

Match the following:

Classify the following angle as right, straight, acute, obtuse, or reflex:

Classify the following angle as right, straight, acute, obtuse, or reflex:

Classify the following angle as right, straight, acute, obtuse, or reflex:

Classify the following angle as right, straight, acute, obtuse, or reflex:

Classify the following angle as right, straight, acute, obtuse, or reflex:

Classify the following angle as right, straight, acute, obtuse, or reflex:

What is the measure of a right angle?

What is the measure of a straight angle?

The measure of an acute angle is < 90°.

The measure of an obtuse angle is < 90°.

The measure of a reflex angle > 180°.

The measure of one complete revolution = 360°.

If m∠A = 53° and m∠B = 35°, then m∠A > m∠B.

Write down the measures of some acute angles.

(give at least two examples).

Write down the measures of some obtuse angles.

(give at least two examples).

Measure the angle given below using the Protractor and write down the measure.

Measure the angle given below using the Protractor and write down the measure.

Measure the angle given below using the Protractor and write down the measure.

Measure the angle given below using the Protractor and write down the measure.

Which angle has a large measure? First estimate and then measure.

Measure of Angle A =

Measure of Angle B =

From these two angles which has larger measure? Estimate and then confirm by measuring them. 

Fill in the blanks with acute, obtuse, right or straight: 

An angle whose measure is less than that of a right angle is ______. 

Fill in the blanks with acute, obtuse, right or straight: 

An angle whose measure is greater than that of a right angle is ______.

Fill in the blanks with acute, obtuse, right or straight: 

An angle whose measure is the sum of the measures of two right angles is ______. 

Fill in the blanks with acute, obtuse, right or straight: 

When the sum of the measures of two angles is that of a right angle, then each one of them is ______. 

Fill in the blanks with acute, obtuse, right or straight: 

When the sum of the measures of two angles is that of a straight angle, and if one of them is acute then the other should be ______. 

Find the measure of the angle shown in figure. (First estimate with your eyes and then find the actual measure with a protractor).

Find the measure of the angle shown in figure. (First estimate with your eyes and then find the actual measure with a protractor).

Find the measure of the angle shown in figure. (First estimate with your eyes and then find the actual measure with a protractor).

Find the measure of the angle shown in figure. (First estimate with your eyes and then find the actual measure with a protractor).

Find the angle measure between the hands of the clock in figure :

9.00 a.m.

Find the angle measure between the hands of the clock in figure :

1.00 p.m.

Find the angle measure between the hands of the clock in figure :

6.00 p.m.

Investigate

In the given figure, the angle measures 30°. Look at the same figure through a magnifying glass.

1. Does the angle become larger?
2. Does the size of the angle change?

Measure and classify each angle :

Let `bar(PQ)` be perpendicular to the line segment `bar(XY)`; Let `bar(PQ)` and `bar(XY)` intersect in point A. What is the measure of ∠PAY?

There are two set-squares in your box. What are the measures of the angles that are formed at their corners? Do they have any angle measure that is common?

Study the diagram. The line l is perpendicular to line m. 

Is CE = EG?

Study the diagram. The line l is perpendicular to line m. 

Does PE bisect CG?

Study the diagram. The line l is perpendicular to line m. 

Identify any two line segments for which PE is the perpendicular bisector.

Study the diagram. The line l is perpendicular to line m. 

Is this true?

AC > FG

Study the diagram. The line l is perpendicular to line m. 

Is this true?

CD = GH

Study the diagram. The line l is perpendicular to line m. 

Is this true?

BC < EH

Name the type of following triangle :

Triangle with lengths of sides 7 cm, 8 cm and 9 cm.

Name the type of following triangle :

∆ABC with AB = 8.7 cm, AC = 7 cm and BC = 6 cm. 

Name the type of following triangle :

∆PQR such that PQ = QR = PR = 5 cm.

Name the type of following triangle :

∆DEF with m∠D = 90° 

Name the type of following triangle :

ΔXYZ with m∠Y = 90° and XY = YZ.

Name the type of following triangle :

ΔLMN with m∠L = 30°, m∠M = 70° and m∠N = 80°

Match the following:

Name the following triangle in two different ways: (you may judge the nature of the angle by observation)

Name the following triangle in two different ways: (you may judge the nature of the angle by observation)

Name the following triangle in two different ways: (you may judge the nature of the angle by observation)

Name the following triangle in two different ways: (you may judge the nature of the angle by observation)

Name the following triangle in two different ways: (you may judge the nature of the angle by observation)

Name the following triangle in two different ways: (you may judge the nature of the angle by observation)

Try to construct triangles using match sticks. Some are shown here.

Can you make a triangle with 3 matchsticks?

(Remember you have to use all the available matchsticks in each case) Name the type of triangle in each case. If you cannot make a triangle, think of reasons for it.

Try to construct triangles using match sticks. Some are shown here.

Can you make a triangle with 4 matchsticks?

(Remember you have to use all the available matchsticks in each case) Name the type of triangle in each case. If you cannot make a triangle, think of reasons for it.

Try to construct triangles using match sticks. Some are shown here.

Can you make a triangle with 5 matchsticks?

(Remember you have to use all the available matchsticks in each case) Name the type of triangle in each case. If you cannot make a triangle, think of reasons for it.

Try to construct triangles using match sticks. Some are shown here.

Can you make a triangle with 6 matchsticks?

(Remember you have to use all the available matchsticks in each case) Name the type of triangle in each case. If you cannot make a triangle, think of reasons for it.

Each angle of a rectangle is a right angle.

The opposite sides of a rectangle are equal in length.

The diagonals of a square are perpendicular to one another.

All the sides of a rhombus are of equal length.

All the sides of a parallelogram are of equal length.

The opposite sides of a trapezium are parallel. 

Give reason for the following :

A square can be thought of as a special rectangle.

Give reasons for the following :

A rectangle can be thought of as a special parallelogram.

Give reasons for the following :

A square can be thought of as a special rhombus.

Give reason for the following :

Squares, rectangles, parallelograms are all quadrilaterals. 

Give reason for the following :

Square is also a parallelogram.

A figure is said to be regular if its sides are equal in length and angles are equal in measure. Can you identify the regular quadrilateral?

Examine whether the following is a polygon. If it is not, say why? 

Examine whether the following is a polygon. If it is not, say why? 

Examine whether the following is a polygon. If it is not, say why? 

Examine whether the following is a polygon. If it is not, say why? 

Name polygon.

Make two more examples of this.

Name polygon.

Make two more examples of this.

Name polygon.

Name polygon.

Make two more examples of this.

Draw a rough sketch of a regular hexagon. Connecting any three of its vertices, draw a triangle. Identify the type of the triangle you have drawn. 

Draw a rough sketch of a regular octagon. (Use squared paper if you wish). Draw a rectangle by joining exactly four of the vertices of the octagon.

A diagonal is a line segment that joins any two vertices of the polygon and is not a side of the polygon. Draw a rough sketch of a pentagon and draw its diagonals.

Match the following :

(a)	Cone	(i)
(b)	Sphere	(ii)
(c)	Cylinder	(iii)
(d)	Cuboid	(iv)
(e)	Pyramid	(v)

Give two examples of shape.

Cone

Give two examples of shape.

Sphere

Give two examples of shape.

Cylinder

Give two examples of shape.

Cuboid

Give two examples of shape.

Pyramid

What shape is your instrument box? 

What shape is a brick?

What shape is a match box?

What shape is a road-roller?

What shape is a sweet laddu?