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Chapter 5 Understanding Elementary Shape Ex 5.5 Solutions

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.

Answer - 1 : -

(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 sides of letter V are inclined at some acute angle on each other.
Hence, (a) and (c) are the models for perpendicular lines.

Question - 2 : - Let  be the perpendicular to the line segment . Let  and  intersect in the point A. What is the measure of ∠PAY?

Answer - 2 : -

From the figure, it can be easily observed that the measure of ∠PAY is 90°.

Question - 3 : - Let  be the perpendicular to the line segment . Let  and  intersect in the point A. What is the measure of ∠PAY?

Answer - 3 : -

From the figure, it can be easily observed that the measure of ∠PAY is 90°.

Question - 4 : - 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 - 4 : - One has a measure of 90°, 45°, 45°.

Other has a measure of 90°, 30°, 60°.
Therefore, the angle of 90° measure is common between them.

Question - 5 : - 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.

Answer - 5 : -

(a) Yes. As CE = EG = 2 units
(b) Yes. PE bisects CG since CE = EG.
(c)   and  
(d) (i) True. As length of AC and FG are of 2 units and 1 unit respectively.
(ii) True. As both have 1 unit length.
(iii) True. As the length of BC and EH are of 1 unit and 3 units respectively.

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