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Tutorialspoint has Published 24147 Articles

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.

Academic Mathematics NCERT Class 6

Tutorialspoint

Updated on 10-Oct-2022 13:34:43

93 Views

To do:We have to give reasons for the given statements.Solution:(a) A rectangle is a quadrilateral in which the opposite sides are parallel and equal to each other and all four angles are right angles. A square is a quadrilateral in which all the sides are equal and all four angles are ... Read More

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?

Academic Mathematics NCERT Class 6

Tutorialspoint

Updated on 10-Oct-2022 13:34:43

70 Views

To do:We have to identify the given regular quadrilateral.Solution:A square is a regular quadrilateral because all the interior angles are right angles and all the sides are equal in length.Therefore,The given regular quadrilateral is a square.

Name each polygon.

Make two more examples of each of these."

Academic Mathematics NCERT Class 6

Tutorialspoint

Updated on 10-Oct-2022 13:34:43

43 Views

To do:We have to name each polygon.Solution:(a) The given figure is a closed figure made of four line segments.Therefore, the given figure is a quadrilateral.Two examples are: (b) The given figure is a closed figure made of three line segments.Therefore, the given figure is a triangle.Two examples are: (c) The given figure ... Read More

Try to construct triangles using match sticks. 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

Academic Mathematics NCERT Class 6

Tutorialspoint

Updated on 10-Oct-2022 13:34:42

130 Views

To do:We have to find the type of triangle that can be made(if possible).Solution:(a) Yes, we can make an equilateral triangle with 3 match sticks.(b) No, we cannot make a triangle with 4 match sticks because the sum of the lengths of any two sides of a triangle is always greater ... Read More

Name the types of following triangles:
(a) Triangle with lengths of sides $ 7 \mathrm{~cm}, 8 \mathrm{~cm} $ and $ 9 \mathrm{~cm} $.
(b) $ \triangle \mathrm{ABC} $ with $ \mathrm{AB}=8.7 \mathrm{~cm}, \mathrm{AC}=7 \mathrm{~cm} $ and $ \mathrm{BC}=6 \mathrm{~cm} $.
(c) $ \triangle \mathrm{PQR} $ such that $ \mathrm{PQ}=\mathrm{QR}=\mathrm{PR}=5 \mathrm{~cm} $.
(d) $ \triangle \mathrm{DEF} $ with $ \mathrm{m} \angle \mathrm{D}=90^{\circ} $
(e) $ \triangle \mathrm{XYZ} $ with $ \mathrm{m} \angle \mathrm{Y}=90^{\circ} $ and $ \mathrm{XY}=\mathrm{YZ} $.
(f) $ \Delta \mathrm{LMN} $ with $ \mathrm{m} \angle \mathrm{L}=30^{\circ}, \mathrm{m} \angle \mathrm{M}=70^{\circ} $ and $ \mathrm{m} \angle \mathrm{N}=80^{\circ} $.

Academic Mathematics NCERT Class 6

Tutorialspoint

Updated on 10-Oct-2022 13:34:41

78 Views

To do:We have to name the types of triangles given.Solution:(a) A scalene triangle is a triangle in which all three sides are of different lengths, and all three angles are of different measures.Therefore, Triangle with lengths of sides $ 7 \mathrm{~cm}, 8 \mathrm{~cm} $ and $ 9 \mathrm{~cm} $ is a ... Read More

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

Academic Mathematics NCERT Class 6

Tutorialspoint

Updated on 10-Oct-2022 13:34:41

467 Views

To do:We have to name each of the given triangles in two different ways.Solution:A scalene triangle is a triangle in which all three sides are of different lengths, and all three angles are of different measures.An isosceles right triangle is a right-angled triangle with an equal base and height.An obtuse-angled triangle is a triangle in which ... Read More

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?

Academic Mathematics NCERT Class 6

Tutorialspoint

Updated on 10-Oct-2022 13:34:39

28 Views

To do:We have to find the measures of the angles that are formed at the corners of two set-squares. Solution:The measures of angles in one of the set squares are $30^o, 60^o$ and $90^o$The measures of angles in the other set square are $45^o, 45^o$ and $90^o$Yes, the $90^o$ angle is ... Read More

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

(a) $ \mathrm{Is} \mathrm{CE}=\mathrm{EG} $ ?
(b) Does PE bisect CG?
(c) Identify any two line segments for which PE is the perpendicular bisector.
(d) Are these true?
(i) $ \mathrm{AC}>\mathrm{FG} $
(ii) $ \mathrm{CD}=\mathrm{GH} $
(iii) \( \mathrm{BC}"

Academic Mathematics NCERT Class 6

Tutorialspoint

Updated on 10-Oct-2022 13:34:39

34 Views

To do:We have to study the diagram and answer the given questions. Solution:The line $ l $ is perpendicular to line $ m $.From the figure, (a) $CE = 2$ units and $EG = 2$ unitsThis implies, $\mathrm{CE}=\mathrm{EG}$(b) $CE = 2$ units, $EG = 2$ unitsThis implies, PE bisects CG.(c) $DE=EF=1$ ... Read More

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.

Academic Mathematics NCERT Class 6

Tutorialspoint

Updated on 10-Oct-2022 13:34:38

46 Views

To do:We have to find which among the given are models for perpendicular lines. Solution:(a) The adjacent edges of a table top are perpendicular to each other.(b) The lines of a railway track are parallel to each other.(c) The line segments forming the letter ‘L’ are perpendicular to each other.(d) The ... Read More

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

Academic Mathematics NCERT Class 6

Tutorialspoint

Updated on 10-Oct-2022 13:34:38

50 Views

Given:$ \overline{\mathrm{PQ}} $ is perpendicular to the line segment $ \overline{\mathrm{XY}} $. $ \overline{\mathrm{PQ}} $ and $ \overline{\mathrm{XY}} $ intersect in the point $ \mathrm{A} $. To do:We have to find the measure of $ \angle \mathrm{PAY} $. Solution: From the figure, The measure of $ \angle \mathrm{PAY} $ is $90^o$. ... Read More

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