Chapter - 5- EXERCISE 5.5 - Basic Geometrical Ideas (NCERT Class 6th Maths Solution)

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

(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 at some acute angle on each other.
Hence, (a) and (c) are the models for perpendicular lines.

2. Let  be the perpendicular to the line segment  . Let and  intersect in the point A. What is the measure of ∠PAY ?

Solution/Explanation:

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/Explanation:

   The set squares in our box  are                                                

                     

Let's measure their angles

so, Angle 90⁰ is common between them. 

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/Explanation:

(a) CE = 5 - 3 = 2 units

     EG = 7 - 5 = 2 units    

     Therefore CE = EG.

(b) CE = EG therefore PE bisects CG.

(c) PE is the perpendicular bisector for line segments DF and BH

(d) (i) AC = 3 - 1 = 2 units

         FG = 7 - 6 = 1 unit

           Therefore AC > FG            True

    (ii) CD = 4 - 3 = 1 unit

         GH = 8 - 7 = 1 unit

          Therefore CD = GH          True    

    (iii) BC = 3 - 2 = 1 unit

          EH = 8 - 5 = 3 units

           Therefore BC < EH            True