NCERT Solutions Class 6th Maths Chapter – 5 Understanding Elementary Shapes 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 a letter ‘L’.
(d) The letter V.

Solution –

(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 forming an acute angle.
Therefore (a) and (c) are models for perpendicular lines.

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

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: BH¯¯ and DF¯¯

(d), (i) True (ii) True (iii) True.