Gujarat Board GSEB Textbook Solutions Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.5 Textbook Questions and Answers.

## Gujarat Board Textbook Solutions Class 6 Maths 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 the letter ‘L’.

(d) The letter V.

Solution:

(a) Yes, the adjacent edges of a table top make a model of perpendicular lines.

(b) No, since parallel lines never intersect Railway track lines do not make a model of perpendicular lines.

(c) Yes, the line segments forming L are perpendicular lines.

(d) No, the line segments forming V, do not represent perpendicular lines.

Question 2.

Let \(\overline{\mathrm{OP}}\) be the perpendicular to the line segment \(\overline{\mathrm{XY}}\). Let \(\overline{\mathrm{PQ}}\) and \(\overline{\mathrm{XY}}\) intersect in the point A. What is the measure of \(\angle PAY \)?

Solution:

Since, \(\overline{\mathrm{OP}}\) ⊥ \(\overline{\mathrm{XY}}\).

Angle between them = 90°

Thus. \(\angle PAY \) = 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 hive any angle measure that is common?

Solution:

The triangles formed by the corners of the two set-squares are given below:

The measures of angles of triangle 1 are: 30°, 60° and 90°

The measures of angles of triangle 2 are: 45°, 45° and 90°

Yes, they have 90° as a common angle.

Question 4.

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

(a) is CE = EG?

(b) Does PE bisect CG?

(c) Identify any two line segments for which PE is the perpendicular bisector.

(d) Ar these true?

(i) AC > FG

(ii) CD = GH

(iii) BC < EH

Solution:

(a) EC = 2 units, EG = 2 units

CE = EG

(b) Yes, PE bisects CG.

(c) \(\overline{\mathrm{BH}}\) and \(\overline{\mathrm{DF}}\)

(d) (i) Yes

(ii) Yes

(iii) Yes