Ncert solutions mathematics class 6 Solutions for Chapter 5 understanding elementary shapes

Exercises in Chapter 5 understanding elementary shapes Grade 6

Exercise 5.1

Exercise 5.2

Exercise 5.3

Exercise 5.4

Exercise 5.5

Exercise 5.6

Exercise 5.7

Exercise 5.8

Exercise 5.9

Questions in Exercise 5.1

Q2) Why is it better to use a divider than a ruler while measuring the length of a line

segment?

Q4)

If A,B,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?

Q5) Verify, whether D is the mid point of AG.

Q6) If B is the midpoint of AC and C is the mid

point of BD, where A, B, C, D lie on a straight line, say why AB = CD?

Q7) 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.

Q1) What is the disadvantage in comparing line

segments by mere observation?

Q3) Draw any line segment, say AB. Take any point C lying in between A and B.

Measure the lengths of AB, BC and AC. Is AB = AC + CB?

What is the disadvantage in 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 AB Take any point C lying in between A and B. Measure the lengths of AB, BC and AC. Is AB = AC + CB?

If A, B, 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 mid point of . AG

If B is the mid point of AC and C is the mid point of BD , where A, B, C, 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.

Questions in Exercise 5.2

Q4)

What part of a revolution have you turned through if you stand to face

(a) east and turn clockwise to face north?

(b) south and turn clockwise to face east?

Q1) What fraction of a clockwise revolution does the hour hand of a clock turn through,

when it goes from

(a) 3 to 9 (b) 4 to 7 (c) 7 to 10

(d) 12 to 9 (e) 1 to 10 (f) 6 to 3

Q5) Find the number of right angles turned through by the hour hand of a clock when

it goes from

(a) 3 to 6 (b) 2 to 8 (c) 5 to 11

(d) 10 to 1 (e) 12 to 9 (f) 12 to 65

Q2)

Where will the hand of a clock stop if it

(a) starts at 12 and makes 1/2 of a revolution, clockwise?

(b) starts at 2 and makes 1/2 of a revolution, clockwise?

(d) starts at 5 and makes 3/4 of a revolution, clockwise?

Q3) Which direction will you face if you start facing

(a) east and make

1/2 of a revolution clockwise?

(b) east and make 11/2 of a revolution clockwise?

Q6) How many right angles do you make if you start facing

(a) south and turn clockwise to the west?

(b) north and turn anti-clockwise to the east?

(d) south and turn to the north?

Q7) Where will the hour hand of a clock stop if it starts

(a) from 6 and turns through 1 right angle?

(b) from 8 and turns through 2 right angles?

(d) from 7 and turns through 2 straight angles?

What fraction of a clockwise revolution does the hour hand of a clock turn through, when it goes from

(a) 3 to 9

(b) 4 to 7

(d) 12 to 9

(e) 1 to 10

(f) 6 to 3

Where will the hand of a clock stop if it

(a) starts at 12 and makes 1 / 2 of a revolution, clockwise?

(b) starts at 2 and makes 1 / 2 of a revolution, clockwise?

(d) starts at 5 and makes 3 / 4 of a revolution, clockwise?

Which direction will you face if you start facing

(a) east and make 1 / 2 of a revolution clockwise?

(b) east and make 1 ½ of a revolution clockwise?

(d) 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

(a) east and turn clockwise to face north?

(b) south 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

(a) 3 to 6

(b) 2 to 8

(d) 10 to 1

(e) 12 to 9

(f) 12 to 6

How many right angles do you make if you start facing

(a) south and turn clockwise to west?

(b) north and turn anti – clockwise to east?

(d) south and turn to north?

Where will the hour hand of a clock stop if it starts

(a) from 6 and turns through 1 right angle?

(b) from 8 and turns through 2 right angles?

(d) from 7 and turns through 2 straight angles?

Questions in Exercise 5.3

Q1) 1. Match the following :

(i) Straight angle (a) Less than one-fourth of a revolution

(ii) Right angle (b) More than half a revolution

(iii) Acute angle (c) Half of a revolution

(iv) Obtuse angle (d) One-fourth of a revolution

(v) Reflex angle (e) Between 1/4 and 1/2 of a revolution

                               (f) One complete revolution

Q2) Classify each one of the following angles as right, straight, acute, obtuse or reflex :

(i) Straight angle -------(a) Less than one-fourth of a revolution

(ii) Right angle ---------(b) More than half a revolution

(iii) Acute angle ---------(c) Half of a revolution

(iv) Obtuse angle ---------(d) One-fourth of a revolution

(v) Reflex angle---------- (e) Between 1 / 4 and 1 / 2 of a revolution

---------------------(f) One complete revolution

Classify each one of the following angles as right, straight, acute, obtuse or reflex:

Questions in Exercise 5.4

Q4) Measure the angles given below using the Protractor and write down the measure.

(a)

(b)

(c)

(d)

Q3) Write down the measures of

(a) some acute angles. (b) some obtuse angles.

(give at least two examples of each).

Q2) 2. Say True or False :

(a) The measure of an acute angle < 90°.

(b) The measure of an obtuse angle < 90°.

(d) The measure of one complete revolution = 360°.

Q5) Which angle has a large measure?

First, estimate and then measure.

The measure of Angle A =

The measure of Angle B =

Q7) Fill in the blanks with acute, obtuse,

right or straight :

(a) An angle whose measure is less

than that of a right angle is__.

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

is _____.

(d) When the sum of the measures of two angles is that of a right angle, then

each one of them is ______.

(e) 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 _______.

Q6) From these two angles which have

larger measure? Estimate and then

confirm by measuring them.

Q8) Find the measure of the angle shown in each figure. (First estimate with your

eyes and then find the actual measurement with a protractor).

Q9) Find the angle measure between the hands of the clock in each figure:

Q10) Investigate

In the given figure, the angle measures 30°. Look

at the same figure through a magnifying glass.

Does the angle become larger? Does the size

of the angle change?

Q11) Measure and classify each angle :

Q1) What is the measure of (i) a right angle? (ii) a straight angle?

What is the measure of

(i) a right angle?

(ii) a straight angle

Say True or False:

(a) The measure of an acute angle < 90°

(b) The measure of an obtuse angle < 90°

(d) The measure of one complete revolution = 360°

(e) If m ∠A = 53° and m ∠B = 350, then m ∠A > m ∠B.

Write down the measures of

(a) some acute angles

(b) some obtuse angles

(give at least two examples of each)

Measures the angles 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:

(a) An angle whose measure is less than that of a right angle is _____

(b) An angle whose measure is greater than that of a right angle is ____

(d) When the sum of the measures of two angles is that of a right angle, then each one of them is_

(e) 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 each 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 each figure:

Investigate

In the given figure, the angle measure 300. Look at the same figure through a magnifying glass. Does the angle becomes larger? Does the size of the angle change?

Measure and classify each angle:

Questions in Exercise 5.5

Q1) Which of the following are models for perpendicular lines:

(a)The adjacent edges of a tabletop.

(b)The lines of a railway track.

(c)The line segments forming the letter ‘L’.

(d)The letter V.

Which of the following are models for perpendicular lines:

(a) The adjacent edges of a table top.

(b) The lines of a railway track.

(d) The letter V.

Let $P Q$ be the perpendicular to the line segment XY.

Let PQ and XY intersect in the point A. What is the measure of ∠PAY?

Q2) Let $\overline{PQ}$ be the perpendicular to the line segment $\overline{XY}$ . Let $\overline{PQ}$ and $\overline{XY}$ intersect in the point A. What is the measure of $\angle PAY$ .

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?

Q3) 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

(a) Is CE = EG?

(b) Does PE bisect CG?

(d) Are these true?

(i) AC > FG

(ii) CD = GH

(iii) BC < EH.

Q4) Study the diagram. The line l is perpendicular to line m.

(a) Is CE = EG?

(b) Does PE bisect CG?

(d) Are these true?

(i) AC > FG

(ii) CD = GH

(iii) BC < EH

Questions in Exercise 5.6

Q1) Name the types of following triangles:

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

(b) $\triangle ABC$ with AB = 8.7 cm, AC = 7 cm and BC = 6 cm.

(d) $\triangle DEF$ with $m\angle D=90\degree$

(e) $\triangle XYZ$ with $m\angle Y=90\degree$ and XY = YZ

(f) $\triangle LMN$ with $m\angle L=30\degree,m\angle M=70\degree\ and\ m\angle N=80\degree$

Name the types of following triangles:

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

(b) ΔABC with AB = 8.7 cm, AC = 7 cm and BC = 6 cm.

(d) ΔDEF with m D∠ = 90°

(e) ΔXYZ with m Y∠ = 90° and XY = YZ.

(f) ΔLMN with m L∠ = 30°, m M∠ = 70° and m N∠ = 80°.

Q2) Match the following:

Match the following:

Measures of Triangle Type of Triangle

(i) 3 sides of equal length ----------(a) Scalene

(ii) 2 sides of equal length-------- (b) Isosceles right angled

(iii) All sides are of different length-----------(c) Obtuse angled

(iv) 3 acute angles---------- (d) Right angled

(v) 1 right angle -----------(e) Equilateral

(vi) 1 obtuse angle ---------(f) Acute angled

(vii) 1 right angle with two sides of equal length-------- (g) Isosceles

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

Q3) Name each of the following triangles in two different ways: (You may judge the nature of angle by observation)

(a)

(b)

(c)

(d)

(e)

(f)

Try to construct triangles using match sticks. Some are shown here. Can you make a triangle with

(a) 3 matchsticks?

(b) 4 matchsticks?

(d) 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

Q4) Try to construct triangles using match sticks. Some are shown here.

Can you make a triangle with:

(a)3 matchsticks?

(b)4 matchsticks?

(d)6 matchsticks?

(Remember you have to use all the available matchsticks in each case)

If you cannot make a triangle, think of reasons for it.

Questions in Exercise 5.7

Q1) Say true or false:

(a)Each angle of a rectangle is a right angle.

(b)The opposite sides of a rectangle are equal in length.

(c)The diagonals of a square are perpendicular to one another.

(d)All the sides of a rhombus are of equal length.

(e)All the sides of a parallelogram are of equal length.

(f)The opposite sides of a trapezium are parallel.

Say True or False:

(a) Each angle of a rectangle is a right angle.

(b) The opposite sides of a rectangle are equal in length.

(d) All the sides of a rhombus are of equal length.

(e) All the sides of a parallelogram are of equal length.

(f) The opposite sides of a trapezium are parallel.

Q2) Give reasons for the following:

(a)A square can be thought of as a special rectangle.

(b)A rectangle can be thought of as a special parallelogram.

(c)A square can be thought of as a special rhombus.

(d)Squares, rectangles, parallelograms are all quadrilateral.

(e)Square is also a parallelogram.

Give reasons for the following:

(a) A square can be thought of as a special rectangle.

(b) A rectangle can be thought of as a special parallelogram.

(d) Squares, rectangles, parallelograms are all quadrilaterals.

(e) Square is also a parallelogram.

Q3) 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?

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?

Questions in Exercise 5.8

Q1) Examine whether the following are polygons. If anyone among these is not, say why?

(a)

(b)

(c)

(d)

Examine whether the following are polygons. If any one among them is not, say why?

Q2) Name each polygon:

(a)

(b)

(c)

(d)

Name each polygon.

Make two more examples of each of these.

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.

Q3) Draw a rough sketch of a regular hexagon. Connecting any three of its vertices, draw a triangle. Identify the type of triangle you have drawn.

Q4) 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.

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.

Q5) 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.

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.

Questions in Exercise 5.9

Q1) Match the following: