**Chapter 5 Understanding Elementary Shapes Ex. 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 a letter ‘L’.

(d) The letter V.

Solution:

(a) Yes, the adjacent edges of a table top are the models of perpendicular lines.

(b) No, the lines of a railway tracks are parallel to each other. So they are not a model for perpendicular lines.

(c) Yes, the two line segments of‘L’ are the model for perpendicular lines.

(d) No, the two line segments of ‘V’ are not a model for perpendicular lines.

Question 2.

Solution:

Since PQ¯¯¯¯¯¯¯¯ ⊥ XY

∴ ∠PAY = 90°

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?

Solution:

The figures of the two set-squares are given below:

The measure angles of triangle (a) are : 30°, 60° and 90°.

The measure angles of triangle (b) are 45°, 45° and 90°.

Yes, they have a common angle of measure 90°.

Question 4.

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

(a) Is CE = EG?

(b) Does PE bisects 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

Solution:

(a) Yes,

Since, CE = 2 units and EG = 2 units

Hence, CE = EG.

(b) Yes, PE bisects CG

(c) Required line segments for which PE is perpendicular bisector are: and

(d) (i) True (ii) True (iii) True