NCERT Solutions For Class 6 Maths Understanding Elementary Shapes Ex 5.5

NCERT Solutions For Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.5

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) 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.
Let $\overline { PQ }$ be the perpendicular to the line segment $\overline { XY }$ . Let $\overline { PQ }$ and $\overline { XY }$ intersect at in the point A. What is the measure of ∠PAY?
Solution:
Since $\overline { PQ }$ ⊥ 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: $\overline { BG }$ and $\overline { DF }$
(d) (i) True (ii) True (iii) True