# Class 6 Maths- Exercise 5.5

1. Which of the following are models for perpendicular lines:

(a) The adjacent edges of a table top

Ans. Figure showing adjacent edges which are perpendicular to each other. Therefore, yes, the adjacent edges of a table top is model of a perpendicular line

(b) The lines of a railway track.

Ans. Figure showing the lines of a railway track which are parallel to each other. Therefore, No the lines of a railway track are not model of a perpendicular line

(c) The line segments forming the letter ‘L’.

Figure showing the line segments forming the letter ‘L’ which are perpendicular to each other.
Therefore, yes, the line segments forming the letter ‘L’ is model of a perpendicular line

(d) The letter V

Ans. Figure showing the letter V which are not perpendicular to each other. They form an acute angle. Therefore, no, the letter V is not a model of a perpendicular line

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

Sol. It is given that PQ is perpendicular to the line segment XY. IT means wherever they intersect, they form a right angle (90o) at the intersecting point.

Here, they intersect at point A.

Hence, PAY = 90o                                                                            Ans.

(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?

Ans. There are two set squares in the box.

The measure of angles in one set square are 300, 600 and 900

The measure of angles in other set square are 450, 450 and 900 Yes, the angle measure 900 is common in both set squares

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

(a) Is CE = EG?
Sol. Here, CE = 2 units and EG = 2 units
Therefore, CE = EG = 2 units
Yes, CE = EG                                                                 Ans.

(b) Does PE bisect CG?
Sol. Here, CE = 2 units and EG = 2 units
Therefore, CE = EG = 2 units
Hence, Yes, PE bisect CG                                            Ans.

(c) Identify any two-line segments for which PE is the perpendicular bisector.
Sol. Perpendicular bisector means forming 90o and also dividing the line segment into two equal parts.
It is given that they are perpendicular to each other
Here, DE = EF = 1 units
And also, BE = EH = 3 units
Therefore, the two line segments for which PE is the perpendicular bisector are DF and BH. Ans.

(d) Are these true?
(i) AC > FG
Ans. True
Reason – From the figure, AC = 2 units and FG = 1 unit
Therefore, yes, AC > FG

(ii) CD = GH
Ans. True
Reason – CD = 1 unit and GH = 1 unit
Therefore, yes, CD = GH

(iii) BC < EH.
Ans. True
Reason – BC = 1 unit and EH = 3 unit Therefore, yes, BC < EH

You cannot copy content of this page