PSEB Class 6 Maths Chapter 9 Understanding Elementary Shapes Questions and Answers Solution
PSEB Punjab Board Class 6 Maths Textbook Solution Chapter 9 Understanding Elementary Shapes Questions and Answers. We have also included some Additional questions, so that students can prepare more strongly.
Exercise 9.1
1.) Measure the line segments using a ruler and a divider.
ANSWER:
Here we have to measure line segment using a ruler and a divider.
Using a ruler = 4.4 cm
Using a divider = 4.4 cm
ANSWER:
Here we have to measure line segment using a ruler and a divider.
Using a ruler = 3.6 cm
Using a divider = 3.6 cm
ANSWER:
Here we have to measure line segment using a ruler and a divider.
Using a ruler = 2.5 cm
Using a divider = 2.5 cm
ANSWER:
Here we have to measure line segment using a ruler and a divider.
Using a ruler = 5.8 cm
Using a divider = 5.8 cm
ANSWER:
Here we have to measure line segment using a ruler and a divider.
Using a ruler = 5 cm
Using a divider = 5 cm
2.) Compare the line segments in the figure and fill in the blanks:
(i) AB —– AB
ANSWER:
From figure,
AB = AB
(ii) CD ——- AC
ANSWER:
From figure,
CD < AC
(iii) AC ——AD
ANSWER:
From figure,
AC > AD
(iv) BC ——– AC
ANSWER:
From figure,
BC < AC
(v) BD —– CD
ANSWER:
From figure,
BD > CD
3.) Draw any line segment AB. Take any point C between A and B. Measure the lengths of AB, BC and AC. Is AB = AC + CB?
ANSWER:
We draw line AB. And taking any point C between A and B
Measuring line segment AB = 6 cm
Measuring line segment AC = 3 cm
Measuring line segment CB = 3 cm
AB = AC + CB
4.) Draw a line segment AB = 5cm and AC = 9cm in such a way that points A, B, C are collinear. What is the length of BC?
ANSWER:
We draw line segment AB = 5cm and AC = 9cm in such a way that points A, B, C are collinear.
Length of BC = Length of AC – Length of AB
Length of BC = 9 cm – 5 cm
Length of BC = 4 cm.
Exercise 9.2
1.) Classify the angles as acute, obtuse, right, straight or reflex angles
ANSWER:
We have to classify angles as acute, obtuse, right, and straight or reflex angles.
We know,
Acute angle = An angle smaller than right angle is acute angle.
Acute angles are (i),(iv) and (x)
We know,
Obtuse angle = Obtuse angle is angle between 900 and 1800
Obtuse angles are (ii) and (vii)
We know,
A right angle measures 90°.
Right angles are (vi) and (viii)
We know,
Straight or reflex angles =
A straight angle measures 180°.
Reflex angle is angle greater than 180°.
Straight or reflex angles are (iii), (iv) and (ix)
2.) Classify the angles:
(i) 80°
(ii) 172°
(iii) 90°
(iv) 0°
(v) 179°
(vi) 215°
(vii) 360°
(viii) 350°
(ix) 15°
(x) 180°
ANSWER:
We have to classify given angles.
Acute angle = an angle smaller than right angle (90°) is acute angle.
Acute angles are 15°, 80°
Obtuse angle = Obtuse angle is angle between 900 and 1800
Obtuse angles are 172°, 179°.
A right angle measures 90°.
Right angles are 90°
A straight angle measures 180°.
Straight angle are 180°
Reflex angle is angle greater than 180°.
Reflex angles are 215°, 350°
Complete angle measures 360°.
Zero angle measures 0°.
3.) Measure the following angles with protractor and write their measurement:
ANSWER:
We have to measure angles with protractor.
Measure of angle = 600
ANSWER:
We have to measure angles with protractor.
Measure of angle = 1250
ANSWER:
We have to measure angles with protractor.
Measure of angle = 1100
ANSWER:
We have to measure angles with protractor.
Measure of angle = 800
ANSWER:
We have to measure angles with protractor.
Measure of angle = 1200
ANSWER:
We have to measure angles with protractor.
Measure of angle = 1050
ANSWER:
We have to measure angles with protractor.
Measure of angle = 800
ANSWER:
We have to measure angles with protractor.
Measure of angle = 1350
ANSWER:
We have to measure angles with protractor.
Measure of angle = 860
ANSWER:
We have to measure angles with protractor.
Measure of angle = 900
4.) How many degrees are there in
(i) Two right angles
ANSWER:
We know,
A right angle measures 90°.
Two right angles = 2 x 90°.
Two right angles = 180°.
(ii) 2/3 right angles
ANSWER:
We know,
A right angle measures 90°.
2/3 right angles = 2/3 x 90°.
2/3 right angles = 60°.
(iii) Four right angles
ANSWER:
We know,
A right angle measures 90°.
Four right angles = 4 x 90°.
Four right angles = 360°.
- What fraction of a clockwise revolution does the hour hand of a clock turn through when it goes from:
(i) 3 to 9
ANSWER:
We have to find fraction of a clockwise revolution does the hour hand of a clock turn through when it goes from 3 to 9.
3 to 9 covers 180°.
3 to 9 covers half or 1/2 clockwise revolution.
(ii) 5 to 8
ANSWER:
We have to find fraction of a clockwise revolution does the hour hand of a clock turn through when it goes from 5 to 8
5 to 8 covers 90°.
5 to 8 covers Quarter or 1/4 clockwise revolution.
(iii) 10 to 4
ANSWER:
We have to find fraction of a clockwise revolution does the hour hand of a clock turn through when it goes from 10 to 4
10 to 4 covers 180°.
10 to 4 covers half or 1/2 clockwise revolution.
(iv) 2 to 11
ANSWER:
We have to find fraction of a clockwise revolution does the hour hand of a clock turn through when it goes from 2 to 11
2 to 11 covers 270°.
2 to 11 covers 3/4 clockwise revolution.
(v) 6 to 3
ANSWER:
We have to find fraction of a clockwise revolution does the hour hand of a clock turn through when it goes from 6 to 3
6 to 3 covers 270°.
6 to 3 covers 3/4 clockwise revolution.
(vi) 2 to 7
ANSWER:
We have to find fraction of a clockwise revolution does the hour hand of a clock turn through when it goes from 2 to 7
2 to 7 covers 150°.
2 to 7 covers 150°/ 360° = 5/12 clockwise revolution.
6.) Find the number of right angles turned through by the hour hand of a clock when it goes clockwise from:
(i) 5 to 8
ANSWER:
We have to find the number of right angles turned through by the hour hand of a clock when it goes clockwise from 5 to 8.
5 to 8 covers 90°.
Number of right angles turned through by the hour hand of a clock when it goes clockwise from 5 to 8 = 1 right angle.
(ii) 1 to 7
ANSWER:
We have to find the number of right angles turned through by the hour hand of a clock when it goes clockwise from 1 to 7
1 to 7 covers 180°.
Number of right angles turned through by the hour hand of a clock when it goes clockwise from1 to 7 = 2 right angle.
(iii) 4 to 10
ANSWER:
We have to find the number of right angles turned through by the hour hand of a clock when it goes clockwise from 4 to 10
4 to 10covers 180°.
Number of right angles turned through by the hour hand of a clock when it goes clockwise from 4 to 10 = 2 right angle.
(iv) 9 to 12
ANSWER:
We have to find the number of right angles turned through by the hour hand of a clock when it goes clockwise from 9 to 12
9 to 12covers 90°.
Number of right angles turned through by the hour hand of a clock when it goes clockwise from 9 to 12 = 1 right angle.
(v) 11 to 2
ANSWER:
We have to find the number of right angles turned through by the hour hand of a clock when it goes clockwise from 11 to 2
11 to 2 covers 90°.
Number of right angles turned through by the hour hand of a clock when it goes clockwise from 11 to 2 = 1 right angle.
(vi) 9 to 6
ANSWER:
We have to find the number of right angles turned through by the hour hand of a clock when it goes clockwise from 9 to 6
9 to 6 covers 270°.
Number of right angles turned through by the hour hand of a clock when it goes clockwise from 9 to 6 = 3 right angle.
(vii) 2 to 11
ANSWER:
We have to find the number of right angles turned through by the hour hand of a clock when it goes clockwise from 2 to 11
2 to 11covers 270°.
Number of right angles turned through by the hour hand of a clock when it goes clockwise from 2 to 11= 3 right angle.
(viii) 10 to 1
ANSWER:
We have to find the number of right angles turned through by the hour hand of a clock when it goes clockwise from 10 to 1
10 to 1 covers 90°.
Number of right angles turned through by the hour hand of a clock when it goes clockwise from 10 to 1 = 1 right angle.
(ix) 12 to 6
ANSWER:
We have to find the number of right angles turned through by the hour hand of a clock when it goes clockwise from 12 to 6
12 to 6covers 180°.
Number of right angles turned through by the hour hand of a clock when it goes clockwise from 12 to 6 = 2 right angle.
(x) 5 to 2
ANSWER:
We have to find the number of right angles turned through by the hour hand of a clock when it goes clockwise from 5 to 2
5 to 2 covers 270°.
Number of right angles turned through by the hour hand of a clock when it goes clockwise from 5 to 2= 3 right angle.
7.) Where will be the hand of a clock stop if it starts at:
(i) 12 and make 1/4 revolution clockwise.
ANSWER:
We have to find where will be the hand of a clock stop if it starts at 12 and make 1/4 revolution clockwise.
We know,
There are total 12 hours in clock.
For 1 revolution it covers 12 hours in clock.
1 revolution = 12 hours
1/4 revolution = ¼ x 12
1/4 revolution = 3 hours.
We add 3 hours in 12 = 3.
Hand of a clock stop at 3.
(ii) 2 and make 1/2 revolution clockwise.
ANSWER:
We have to find where will be the hand of a clock stop if it starts at 2 and make 1/2 revolution clockwise.
We know,
There are total 12 hours in clock.
For 1 revolution it covers 12 hours in clock.
1 revolution = 12 hours
1/2 revolution = 1/2 x 12
1/2 revolution = 6 hours.
We add 6 hours in 2 = 8.
Hand of a clock stop at 8.
(iii) 5 and make 1/4 revolution clockwise.
ANSWER:
We have to find where will be the hand of a clock stop if it starts at5 and make 1/4 revolution clockwise.
We know,
There are total 12 hours in clock.
For 1 revolution it covers 12 hours in clock.
1 revolution = 12 hours
1/4 revolution = 1/4 x 12
1/4 revolution = 3 hours.
We add 3 hours in 5 = 8.
Hand of a clock stop at 8.
(iv) 5 and make 3/4 revolution clockwise.
ANSWER:
We have to find where will be the hand of a clock stop if it starts at5 and make 3/4 revolution clockwise.
We know,
There are total 12 hours in clock.
For 1 revolution it covers 12 hours in clock.
1 revolution = 12 hours
3/4 revolution = 3/4 x 12
3/4 revolution = 9 hours.
We add 9 hours in 5 = 2.
Hand of a clock stop at 2.
8.) What part of revolution have you turned through if you stand facing.
(i) East and turn clockwise to north.
ANSWER:
We have to find part of revolution have you turned through when you facing East and turn clockwise to north.
We have to turn 3/4 revolution when we facing East and turn clockwise to north.
(ii) South and turn clockwise to north.
ANSWER:
We have to find part of revolution have you turned through when you facing South and turn clockwise to north.
We have to turn 1/2 revolution when we facingSouth and turn clockwise to north.
(iii) South and turn clockwise to east.
ANSWER:
We have to find part of revolution have you turned through when you facing South and turn clockwise to east
We have to turn 3/4 revolution when we facing South and turn clockwise to east.
(iv) West and turn clockwise to east.
ANSWER:
We have to find part of revolution have you turned through when you facing West and turn clockwise to east.
We have to turn 1/2 revolution when we facingWest and turn clockwise to east.
9.) Find the angle measure between the hands of the clock in each figure:
ANSWER:
We have to find angle between 12 and 3.
We know,
In 1 hour there is 300
Total 3 hours = 3 x 300
Angle between 12 and 3 = 900
ANSWER:
We have to find angle between 12 and 6.
We know,
In 1 hour there is 300
Total 6 hours = 6 x 300
Angle between 12 and 6 = 1800
ANSWER:
We have to find angle between 12 and 2.
We know,
In 1 hour there is 300
Total 2 hours = 2 x 300
Angle between 12 and 2 = 600
10.) Draw the following angles by protractor:
(i) 40°
ANSWER:
We have to draw 40° by protractor.
Angle ABC = 400
(iv) 90°
ANSWER:
We have to draw 90° by protractor.
Angle ABC = 900
(v) 130°
ANSWER:
We have to draw 130° by protractor.
Angle ABC = 1300
11.) State true or false:
(i) The sum of two right angles is always a straight angle.
ANSWER:
True.
(ii) The sum of two acute angles is always a reflex angle.
ANSWER:
False.
(iii) The obtuse angle has measurement between 90° to 180°
ANSWER:
True.
(iv) A complete revolution has four right angles.
ANSWER:
True.
12.) Fill in the blanks:
(i) The angle which is greater than 0° and less than 90° is called ———–
ANSWER:
The angle which is greater than 0° and less than 90° is called acute angle.
(ii) The angle whose measurement equal to two right angle is ————
ANSWER:
The angle whose measurement equal to two right angle is straight angle.
(iii) The angle between 90° and 180° is —————-
ANSWER:
The angle between 90° and 180° is obtuse angle.
Exercise 9.3
1.) Identify the shape having perpendicular lines:
ANSWER:
We know,
When two lines intersect and the angle between them is a right angle, then the lines are said to be perpendicular.
We have to find shape having perpendicular lines
Perpendicular line shapes are (ii),(iii) and (v).
2.) Identify the examples having perpendicular lines:
(i) Lines of railway track.
(ii) Adjacent edges of a table.
(iii) Line segment forming letter ‘L’.
ANSWER:
We know,
When two lines intersect and the angle between them is a right angle, then the lines are said to be perpendicular.
The examples having perpendicular lines are
(ii) Adjacent edges of a table.
(iii) Line segment forming letter ‘L’.
- Let AB be perpendicular to PQ and they intersect at O. What is the measure of ANGLE AOP.
ANSWER:
We know,
When two lines intersect and the angle between them is a right angle, then the lines are said to be perpendicular.
ANGLE AOP = 900
4.) Line m is perpendicular to line & in the given figure. Each point on the line ( is marked at equal intervals. Study the diagram and state true or false.
(i) Line m is bisector of line segment AI
ANSWER:
From figure,
Line m is bisector of line segment AI
True.
(ii) CE=EF
ANSWER:
From figure,
CE is not equal to EF
False.
(iii) DF = 2DE
ANSWER:
From figure,
DF = 2DE
True.
Exercise 9.4
1.) Classify each of the following triangles as scalene, isosceles or equilateral:
ANSWER:
We have to classify triangles as scalene, isosceles or equilateral.
We know,
A triangle having all three unequal sides is called a Scalene Triangle
Scalene Triangle are figure (iii) and (v)
A triangle having two equal sides is called an Isosceles Triangle
Isosceles Triangle are figures (i) and (iv)
A triangle having three equal sides is called an Equilateral Triangle
Equilateral Triangleare figures (ii) and (vi)
2.) Classify each of the following triangles as acute, obtuse or right triangle:
ANSWER:
We have to classify triangles as acute, obtuse or right triangle.
We know,
If each angle is less than 90°, then the triangle is called an acute angled triangle.
Acute angled triangles are (iii) and (vi)
If any one angle is a right angle then the triangle is called a right angled triangle.
Right angled triangle are (ii) and (iv)
If any one angle is greater than 90°, then the triangle is called an obtuse angled triangle.
Obtuse angled triangle are (i) and (v)
3.) Which of the following triangles are possible with the given angles?
(i) 60°, 60°, 60°
ANSWER:
We know,
Sum of angles of a triangle is 1800
60°+ 60°+ 60° = 1800
This triangle is possible.
(ii) 110°, 50°, 30°
ANSWER:
We know,
Sum of angles of a triangle is 1800
110°+ 50°+ 30°= 1900
This triangle is not possible.
(iii) 65°, 55°, 60°
ANSWER:
We know,
Sum of angles of a triangle is 1800
65°+ 55°+ 60= 1800
This triangle is possible.
(iv) 90°, 40°, 50°
ANSWER:
We know,
Sum of angles of a triangle is 1800
90°+ 40°+ 50°= 1800
This triangle is possible.
(v) 48°, 62°, 50°
ANSWER:
We know,
Sum of angles of a triangle is 1800
48°+ 62°+ 50° = 1600
This triangle is not possible.
(vi) 90°,95°,30°
ANSWER:
We know,
Sum of angles of a triangle is 1800
90°+ 95°+ 30° = 2150
This triangle is not possible.
4.) Classify each of the following triangles as scalene, isosceles or equilateral triangle:
(i) 4cm, 5cm, 6cm
ANSWER:
A triangle having all three unequal sides is called a Scalene Triangle
4cm, 5cm, 6cm = This is a Scalene Triangle.
(ii) 5cm, 7cm, 5cm
ANSWER:
A triangle having two equal sides is called an Isosceles Triangle
5cm, 7cm, 5cm = Isosceles Triangle
(iii) 4.2m. 5.3m, 6.1m
ANSWER:
A triangle having all three unequal sides is called a Scalene Triangle
4.2m. 5.3m, 6.1m= This is a Scalene Triangle.
(iv) 3.5cm, 3.5cm, 3.5cm
ANSWER:
A triangle having three equal sides is called an Equilateral Triangle
3.5cm, 3.5cm, 3.5cm = Equilateral Triangle
(v) 8cm, 4.2cm, 4.2cm
ANSWER:
A triangle having two equal sides is called an Isosceles Triangle
8cm, 4.2cm, 4.2cm = Isosceles Triangle
(vi) 2cm, 3cm, 4cm
ANSWER:
A triangle having all three unequal sides is called a Scalene Triangle
2cm, 3cm, 4cm= This is a Scalene Triangle.
5.) Name the following triangles in both ways:
(Based on sides and angles)
ANSWER:
A triangle having all three unequal sides is called a Scalene Triangle
This is a Scalene Triangle.
If each angle is less than 90°, then the triangle is called an acute angled triangle.
This is aacute angled triangle.
ANSWER:
A triangle having two equal sides is called an Isosceles Triangle
This is a Isosceles Triangle.
If any one angle is a right angle then the triangle is called a right angled triangle.
This is a right angled triangle.
ANSWER:
A triangle having two equal sides is called an Isosceles Triangle
This is a Isosceles Triangle.
If any one angle is greater than 90°, then the triangle is called an obtuse angled triangle.
This is a obtuse angled triangle.
ANSWER:
A triangle having three equal sides and three equal angles is called an Equilateral Triangle
ANSWER:
A triangle having all three unequal sides is called a Scalene Triangle
This is a Scalene Triangle.
If any one angle is greater than 90°, then the triangle is called an obtuse angled triangle.
This is a obtuse angled triangle.
6.) Fill in the blanks:
(i) A triangle has ———- sides.
ANSWER:
A triangle has 3 sides.
(ii) A triangle has ———- vertices.
ANSWER:
A triangle has 3 vertices.
(iii) A triangle has ———— angles.
ANSWER:
A triangle has 3angles.
(iv) A triangle has —————– parts.
ANSWER:
A triangle has 6 parts.
(v) A triangle whose all sides are different is known as ———-
ANSWER:
A triangle whose all sides are different is known as Scalene Triangle
(vi) A triangle whose all angles are acute is known as ———-
ANSWER:
A triangle whose all angles are acute is known asacute angled triangle
(vii) A triangle whose two sides are equal is known as —————
ANSWER:
A triangle whose two sides are equal is known as Isosceles Triangle
(viii) A triangle whose one angle is obtuse is known as ———–
ANSWER:
A triangle whose one angle is obtuse is known asobtuse angled triangle.
(ix) A triangle whose all sides are equal is known as ————–
ANSWER:
A triangle whose all sides are equal is known asEquilateral Triangle
(x) A triangle whose one angle is right angle is known as —————–
ANSWER:
A triangle whose one angle is right angle is known asright angled triangle.
7.) State True or False:-
(i) Each equilateral triangle is an isosceles triangle.
ANSWER:
True.
(ii) Each acute angled triangle is a scalene triangle.
ANSWER:
False.
(iii) Each isosceles triangle is an equilateral triangle.
ANSWER:
False.
(iv) There are two obtuse angles in an obtuse triangle.
ANSWER:
False.
(v) In right triangle, there is only one right angle.
ANSWER:
True.
(vi) Right triangle can never be isosceles.
ANSWER:
False.