Understanding Elementary Shapes-Solutions Ex-5.5

CBSE Class –VI Mathematics
NCERT Solutions
Chapter 5 Understanding Elementary Shapes (Ex. 5.5)

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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: (a) Perpendicular

(b) Not perpendicular, they are parallel

(c) Perpendicular

(d) Not perpendicular

Question 2. Let PQ¯¯¯¯¯¯¯$\overline{\text{PQ}}$ be the perpendicular to the line segment XY¯¯¯¯¯¯¯¯.$\overline{\text{XY}}.$ Let PQ¯¯¯¯¯¯¯$\overline{\text{PQ}}$ and XY¯¯¯¯¯¯¯¯$\overline{\text{XY}}$ intersect in the point A. What is the measure of ∠$\mathrm{\angle }$PAY.

Answer: Sol.

∠$\mathrm{\angle }$PAY = 90∘${90}^{\circ }$

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?
Answer: One set-square has 45o,90o,45o  and other set-square has 60o,90o,30o . They have 90o as common angle.

Question 4. Study the diagram. The line l$l$ is perpendicular to line m.$m.$

(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: (a) Yes, both measure 2 units.

(b) Yes, because CE = EG

(c) DF¯¯¯¯¯¯¯$\overline{\text{DF}}$ and CG¯¯¯¯¯¯¯¯$\overline{\text{CG}}$, BH¯¯¯¯¯¯¯$\overline{\text{BH}}$

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