CBSE Class 6

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.8 are part of NCERT Solutions for Class 6 Maths. Here we have given NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.8.

• Understanding Elementary Shapes Class 6 Ex 5.1
• Understanding Elementary Shapes Class 6 Ex 5.2
• Understanding Elementary Shapes Class 6 Ex 5.3
• Understanding Elementary Shapes Class 6 Ex 5.4
• Understanding Elementary Shapes Class 6 Ex 5.5
• Understanding Elementary Shapes Class 6 Ex 5.6
• Understanding Elementary Shapes Class 6 Ex 5.7
• Understanding Elementary Shapes Class 6 Ex 5.9

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.8

Question 1.
Examine whether the following are polygons. If anyone among them is not, say why?

Solution :
(a) is not a closed figure and hence is not a polygon.
(b) is a polygon of six sides.
(c) is not a polygon since it is not made of line segments.
(d) is not a polygon since it is not made of line segments.

Question 2.
Name each polygon:

Make two more examples of each of these.
Solution :
(a) A Quadrilateral
(b) A Triangle
(c) A Pentagon (5-sided)
(d) An Octagon (8-sided).

Question 3.
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.
Solution :

The triangle ABC drawn is an obtuse-angled isosceles triangle.

Question 4.
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.
Solution :

Question 5.
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.
Solution :

We hope the NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.8 help you. If you have any query regarding NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.8, drop a comment below and we will get back to you at the earliest.

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.7 are part of NCERT Solutions for Class 6 Maths. Here we have given NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.7.

• Understanding Elementary Shapes Class 6 Ex 5.1
• Understanding Elementary Shapes Class 6 Ex 5.2
• Understanding Elementary Shapes Class 6 Ex 5.3
• Understanding Elementary Shapes Class 6 Ex 5.4
• Understanding Elementary Shapes Class 6 Ex 5.5
• Understanding Elementary Shapes Class 6 Ex 5.6
• Understanding Elementary Shapes Class 6 Ex 5.8
• Understanding Elementary Shapes Class 6 Ex 5.9

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.7

Question 1.
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.
Solution :
(a) True
(b) True
(c) True
(d) True
(e) False
(f) False.

Question 2.
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 quadrilaterals.
(e) Square is also a parallelogram.
Solution :
(a) A rectangle with all sides equal becomes a square.
(b) A parallelogram with each angle a right angle becomes a rectangle.
(c) A rhombus with each angle a right angle becomes a square.
(d) All these are four-sided polygons made of line segments.
(e) The opposite sides of a square are parallels, so it is a parallelogram.

Question 3.
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?
Solution :
A square is a regular quadrilateral.

We hope the NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.7 help you. If you have any query regarding NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.7, drop a comment below and we will get back to you at the earliest.

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.6 are part of NCERT Solutions for Class 6 Maths. Here we have given NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.6.

• Understanding Elementary Shapes Class 6 Ex 5.1
• Understanding Elementary Shapes Class 6 Ex 5.2
• Understanding Elementary Shapes Class 6 Ex 5.3
• Understanding Elementary Shapes Class 6 Ex 5.4
• Understanding Elementary Shapes Class 6 Ex 5.5
• Understanding Elementary Shapes Class 6 Ex 5.7
• Understanding Elementary Shapes Class 6 Ex 5.8
• Understanding Elementary Shapes Class 6 Ex 5.9

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.6

Question 1.
Name the types of following triangles:
(a) Triangle with lengths of sides 7 cm, 8 cm and 9 cm.
(b) ΔABC with AB = 8.7cm, AC =7cm andBC = 6 cm.
(c) ΔPQR such that PQ = QR = PR = 5 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°.
Solution :
(a) Scalene triangle
(b) Scalene triangle
(c) Equilateral triangle
(d) Right angled triangle
(e) Isosceles right triangle
(f) Acute angled triangle.

Question 2.
Match the following :

Solution :

Question 3.
Name each of the following triangles in two different ways : (you may judge the nature of the angle by observation).


Solution :
(a) Acute-angled and isosceles.
(b) Right-angled and scalene.
(c) Obtuse-angled and isosceles.
(d) Right-angled and isosceles.
(e) Equilateral and acute-angled.
(f) Obtuse-angled and scalene.

Question 4.
Try to construct triangles using matchsticks. Some are shown here. Can you make a triangle with

(a) 3 matchsticks?
(b) 4 matchsticks?
(c) 5 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.
Solution :
(a) Yes, an equilateral triangle.
(b) No, since the sum of the lengths of any two sides of a triangle is always greater than the length of the third side.
(c) Yes, an isosceles triangle.
(d) Yes, an equilateral triangle.

We hope the NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.6 help you. If you have any query regarding NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.6, drop a comment below and we will get back to you at the earliest.

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.5 are part of NCERT Solutions for Class 6 Maths. Here we have given NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.5.

• Understanding Elementary Shapes Class 6 Ex 5.1
• Understanding Elementary Shapes Class 6 Ex 5.2
• Understanding Elementary Shapes Class 6 Ex 5.3
• Understanding Elementary Shapes Class 6 Ex 5.4
• Understanding Elementary Shapes Class 6 Ex 5.6
• Understanding Elementary Shapes Class 6 Ex 5.7
• Understanding Elementary Shapes Class 6 Ex 5.8
• Understanding Elementary Shapes Class 6 Ex 5.9

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.5

Question 1.
Which of the following are models for perpendicular lines :
(a) The adjacent edges of a table top.
(b) The lines of a railway track.
(c) The line segments forming the letter “L”.
(d) The letter V.
Solution :
(a) and (c) are models for perpendicular lines.

Question 2.
Let \(\overline { PQ }\) be the perpendicular to the line segment \(\overline { XY }\) . Let \(\vec { PQ }\) and \(\overline { XY }\) intersect in the point A. What is the measure of ∠PAY ?
Solution :
The measure of ∠PAY is 90°.

Question 3.
There are two “set-squares ” in your box. What are the measures of the angles that are formed at their comers? Do they have any angle measure that is common?
Solution :
One is a 30° – 60° – 90° set square; the other is a 45° – 45° – 90° set square. The angle of measure 90° (i.e., a right angle) is common between them.

Question 4.
Study the diagram. The line l is perpendicular to line m.

(a) Is CE = EG?
(b) Does PE bisect CG?
(c) Identify any two line segments for which PE is the perpendicular bisector.
(d) Are these true?
(i) AC > EG
(ii) CD = GH
(iii) BC < EH.
Solution :
(a) CE= CD + DE
= 1 + 1=2 units
EG = EF + FG
= 1 + 1=2 units
∴ CE= EG

(b) ∴ CE = EG
∴ E is the mid-point of CG.
∴ Line PE bisects line segment CG

(c) ∴ DE = EF = 1 unit
∴ PE is the perpendicular bisector of line segment DF
∴ BE = EH = 3 units
∴ PE is the perpendicular bisector of BH

(d)
(i) true
(ii) true
(iii) true

We hope the NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.5 help you. If you have any query regarding NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.5, drop a comment below and we will get back to you at the earliest.

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.4 are part of NCERT Solutions for Class 6 Maths. Here we have given NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.4.

• Understanding Elementary Shapes Class 6 Ex 5.1
• Understanding Elementary Shapes Class 6 Ex 5.2
• Understanding Elementary Shapes Class 6 Ex 5.3
• Understanding Elementary Shapes Class 6 Ex 5.5
• Understanding Elementary Shapes Class 6 Ex 5.6
• Understanding Elementary Shapes Class 6 Ex 5.7
• Understanding Elementary Shapes Class 6 Ex 5.8
• Understanding Elementary Shapes Class 6 Ex 5.9

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.4

Question 1.
What is the measure of
(i) a right angle
(ii) a straight angle?
Solution :
(i) The measure of a right angle is 90°.
(ii) The measure of a straight angle is 180°.

Question 2.
Say True or False:
(a) The measure of an acute angle < 90°.
(b) The measure of an obtuse angle of < 90°.
(c) The measure of reflex angle > 180°.
(d) The measure of one complete revolution = 360°.
(e) If m∠A = 53° and m∠B = 35°, then m∠A > m∠B.
Solution :
(a) True
(b) False
(c) True
(d) True
(e) True.

Question 3.
Write down the measures of
(a) some acute angles.
(b) some obtuse angles. (give at least two examples of each).
Solution :
(a) 23°, 89°
(b) 91°, 179°.

Question 4.
Measure the angles given below, using the Protractor and write down the measure.

Solution :
(a) 45°
(b) 125°
(e) 90°
(d) ∠l = 40°, ∠2 = 125° and ∠3 = 95°.

Question 5.
Which angle has a large measure? First, estimate and then measure.

Measure of angle A =
Measure of angle B =
Solution :
Measure of angle A = 40°
Measure of angle B = 65°
The angle B has a larger measure.

Question 6.
From these two angles which have larger measure? Estimate and then confirmed by the measuring them.

Solution :
Measure of first angle = 45°
Measure of second angle = 60°
The second angle has larger measure.

Question 7.
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. ____________
(c) An angle whose measure is the sum of the measures of two right angles 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 than the other should be ____________.
Solution :
(a) An angle whose measure is less than that of a right angle is an acute angle.
(b) An angle whose measure is greater than that of a right angle is the obtuse angle (if the angle is less than 180°)
(c) An angle whose measure is the sum of the measures of two right angles is the straight angle.
(d) When the sum of the measures of two angles is that of a right angle, then each one of them is acute.
(e) When the sum of the measures of two angles is that of a straight angle and if one of them is acute than the other should be an obtuse angle.

Question 8.
Find the measure of the angle shown in each figure. (First, estimate with your eye, and then find the actual measurements with a protractor).
(a)

(b)

(c)

(d)

Solution :
Estimation with eye
(a) 45°
(b) 125°
(c) 60°
(d) 135° actual measure with a protractor
Solution :
(a) 40°
(b) 130°
(c) 65°
(d) 135°

Question 9.
Find the angle measure between the hands of the clock in each figure :

Solution :

• 90°
• 30°
• 180°.

Question 10.
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?
Solution :
No!; No!

Question 11.
Measure and classify each angle :

Solution :
Angle ∠AOB ∠AOC ∠BOC ∠DOC ∠DOA ∠DOB Measure 40° 120° 80° 105° 140° 180° Type acute obtuse acute obtuse straight.

We hope the NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.4 help you. If you have any query regarding NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.4, drop a comment below and we will get back to you at the earliest.