� 6^TH MATHS�CHAPTER 05�UNDERSTANDING ELEMENTRY SHAPES

EXERCISE 5.1

• Question 1:
• What is the disadvantage in comparing line segments by mere observation?

• Answer 1:
• There may be chance of error due to improper viewing.

• Question 2:
• Why is it better to use a divider than a ruler, while measuring the length of a line segment?

• Answer 2:
• It is better to use a divider than a ruler, because the thickness of the ruler may cause difficulties in reading of his length.
• However divider gives up accurate measurement.

• Question 3:
• 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?

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• [Note: If A, B, 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.]

• Answer 3:
• Yes.

• Question 4:
• If A, B, C are three points on a line such that AB = 5 cm, BC = 3cm and AC = 8 cm,
• which one of them lies between the other two?

• Answer 4:
• AC is the longest line segment, thus B is the point between A and C.

• Question 7:
• Draw five triangles and measure their sides.
• Check in each case, of the sum of the lengths of any two sides is always less than the third side.

• Answer 7:
• Yes, sum of two sides of a triangle is always greater than the third side.

� EXERCISE 5.2

Question 1:

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

Answer 3:

(a) West (b) West (c) North (d) South

(For answer (d), it is immaterial whether we turn clockwise or anticlockwise, because one full revolution will bring us back to the original position)

Question 4:

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?

(c) West and turn clockwise to face east?

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Question 5:

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 6

Answer 5:

(a) One right angle

(b) Two right angles

(c) Two right angles

(d) One right angle

(e) Three right angles

(f) Two right angles

Question 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?

(c) West and turn to west?

(d) South and turn to north?

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Answer 6:

(a) One right angle (b) Three right angles

(c) Four right angles (d) Two right angles

Question 7:

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?

(c) from 10 and turns through 3 right angles?

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

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Answer 7:

(a) At 9 (b) At 2

(c) At 7 (d) At 7

� EXERCISE 5.3

• Question 2:
• Classify each one of the following angles as right, straight, acute, obtuse or reflex:

EXERCISE 5.4

Question 1:

What is the measure of

(i) a right angle?

(ii) a straight angle?

Question 3:

Write down the measure of:

(a) some acute angles

(b) some obtuse angles

(give at least two examples of each)

• Question 4:
• Measure the angles given below, using the protractor and write down the measure:

Question 5:

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

Measure of angle A =

Measure of angle B =

• Question 6:
• From these two angles which has larger measure?
• Estimate and then confirm by measuring them:

Answer 6:

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 then the other should be ________________.

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Answer 7:

(a) acute angle

(b) obtuse angle

(c) straight angle

(d) acute angle

(e) obtuse angle

Question 8:

Find the measure of the angle shown in each figure.

(First estimate with your eyes and then find the actual measure with a protractor).

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

Question 10:

Investigate:

In the given figure, the angle measure 30° .

Look at the same figure through a magnifying glass. Does the angle becomes larger?

Does the size of the angle change?

• Answer 10:
• No, the measure of angle will be same.

• Question 11:
• Measure and classify each angle:

EXERCISE 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.

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• Answer 2:

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• Question 3:
• 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?

• Answer 3:

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EXERCISE 5.6

Question 3:

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

EXERCISE 5.7

Answer 2:

(a) Because its all angles are right angle and opposite sides are equal.

(b) Because its opposite sides are equal and parallel.

(c) Because its four sides are equal and diagonals are perpendicular to each other.

(d) Because all of them have four sides.

(e) Because its opposite sides are equal and parallel.

• 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?

• Answer 3:
• A square is a regular quadrilateral.

EXERCISE 5.8

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

• Question 2:
• Name each polygon:

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• Make two more examples of each of these.

Answer 2:

(a) Quadrilateral

(b) Triangle

(c) Pentagon

(d) Octagon

• 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.

• Answer 3:
• ABCDEF is a regular hexagon and triangle thus formed by joining AEF is an isosceles triangle.

• Question 4:
• 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.

• Answer 4:
• ABCDEFGH is a regular octagon and CDGH is a rectangle.

• 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.

• Answer 5:
• ABCDE is the required pentagon and its diagonals are AD, AC, BE and BD.

EXERCISE 5.9

THANKS