Solution of Chapter 5. Understanding Elementary Shapes (NCERT - Mathematics Book)

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?

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 and C is the mid-point of, 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.

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

Where will the hand of a clock stop if it.

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

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

(c) starts at 5 and makes of a revolution, clockwise?

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

Which direction will you face if you start facing

(a) east and makeof a revolution clockwise?

(b) east and make of a revolution clockwise?

(c) west and make of a revolution clockwise?

(d) south and make one full revolution?

(Should we specify clockwise or anti-clockwise for this 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?

(c) west 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

(c) 5 to 1 (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?

(c) west and turn to west?

(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?

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

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

Match the following:

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

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°.

(c) The measure of a 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.

Write down the measures of

(a) some acute angles.

(b) some obtuse angles.

(Give two examples of each).

Measure 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 ∠A =

Measure of ∠B =

From the following two angles, which has longer 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 ………… .

(c) An angle whose measure is the sum of the measure of two 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 measures 30°. Look at the same figure through a magnifying glass.

Does the angle become larger? Does the size of the angle change?

Measure and classify each angle:

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.

Let be the perpendicular to the line segment. Let and intersect in the point A. What is the measure of ∠PAY?

There are two set-squares in your geometry 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?

(c) Identify any two line segments for which PE is the perpendicular bisector.

(d) Are these true?

(i) AC > FG (ii) CD = GH (iii) BC < EH.

Name the types of following triangles:

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

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

(c) Δ PQR such that PQ = QR = PR = 5 cm.

(d) Δ DEF with m ∠D = 90°.

(e) Δ XYZ with m∠Y = 90° and XY = YZ.

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

Match the following:

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

(a)

(b)

(c)

(d)

(e)

(f)

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 reason for it.

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.

Give reason 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.

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?

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

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.

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.

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.

Match the following:

Give two more examples of each shape.

What shape is

(a) Your instrument box

(b) A brick?

(c) A match box?

(d) A road-roller?

(e) A sweet laddu?