## MP Board Class 6th Maths Solutions 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) Perpendicular

(b) Not perpendicular

(c) Perpendicular

(d) Not perpendicular

Question 2.

Let \(\overline{P Q}\) be the perpendicular to the line segment \(\overline{X Y}\). Let \(\overline{P Q}\) and \(\overline{X Y}\) intersect in the point A. What is the measure of ∠PAY?

Solution:

∠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:

One set-square has angles 45°, 90°, 45° and other set-square has angles 60°, 90°, 30°.

Yes, they have angle measure 90° as common.

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) Are these true?

(i) AC>FG

(ii) CD = GH

(iii) BC < EH.

Solution:

(a) Yes, both measure 2 units.

(b) Yes, because CE = EG

(c) \(\overline{B H}\) and \(\overline{D F}\) are two line segments for which PE is the perpendicular bisector.

(d) (i) True

Since, AC = 2 units and FG = 1 unit.

∴ AC > FG

(ii) True

Since, CD = GH = 1 unit

(iii) True

Since, BC = 1 unit, EH = 3 units.

∴ BC < EH.