NCERT Solutions for Class 6 Maths Chapter 5: Understanding Elementary Shapes - Exercise 5.5

Exercise 5.5

1. Which of the following are models for perpendicular lines?

1. The adjacent edges of a table top.

Ans:  The adjacent legs of a table top make an angle of $90^\circ $ with each other. 

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Hence, they are perpendicular.

2. The lines of a railway track.

Ans: The lines of a railway track do not meet each other. Thus, no $90^\circ $ angle is formed. Hence, the lines of railway track are not perpendicular. The following diagram shows that the lines of the railway track are not perpendicular.

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3. The line segments forming the letter ‘L’

Ans:  The line segments that form the letter L, form a $90^\circ $ degree angle.

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Hence, they are perpendicular to each other.

4. The letter V.

Ans:  The letter V has no right angle. 

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Hence, this model is not perpendicular.

2. Let $PQ$ be the perpendicular to the line segment  $XY$.  Let $PQ$ and  $XY$  intersect in the point $A$. What is the measure of $\angle PAY$?

Ans:  We will represent the given data through a diagram.

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Since PQ is perpendicular to XY, then, $\angle PAY = 90^\circ $.

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?

Ans:  The set squares form two types of angles.

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One of the set squares has angles of measure,$45^\circ $, $90^\circ $, $45^\circ $,  and the other set square has angles of measure, $60^\circ $,$90^\circ $,$30^\circ $. Thus, they have $90^\circ $ as a common angle.

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

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1. Is $CE = EG$?

Ans:  Observe from the number line that $CE$ is 2 units and $EG$ is 2 units. Hence, 

$CE = EG$.

2. Does $PE$ bisect $CG$?

Ans:  As $CE = EG$, this implies that $PE$ divides $CG$ into two equal parts. Hence,

$PE$ bisect $CG$.

3. Identify any two-line segments for which $PE$ is the perpendicular bisector.

Ans: A perpendicular bisector bisects the line segment at $90^\circ $. Observe that $PE$divides $DF$ into two segments of one unit, namely, $DE$ and $EF$. Similarly, $PE$divides $CG$ into two segments of one unit, namely, $CE$ and $EG$. 

4. Are the following expressions true?

1. $AC > FG$.

Ans:  From the figure, $AC$ measures 2 units and $FG$ measures 1 unit. Thus, $2 > 1$. So, $AC > FG$. Hence, the given relation is true.

2. $CD = GH$

Ans: From the figure, $CD$ is 1 unit and $GH$ is 1 unit. So,$CD = GH = 1\,\,{\text{unit}}$. Hence, the given relation is true.

3. $BC < EH$

Ans:  From the figure, $BC$ is 1 unit and $EH$ is $4$ unit. Thus, $1 < 4$. Hence, $BC < EH$. Therefore, the given relation is true.

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes (Ex 5.5) Exercise 5.5

Opting for the NCERT solutions for Ex 5.5 Class 6 Maths is considered as the best option for the CBSE students when it comes to exam preparation. This chapter consists of many exercises. Out of which we have provided the Exercise 5.5 Class 6 Maths NCERT solutions on this page in PDF format. You can download this solution as per your convenience or you can study it directly from our website/ app online.

Vedantu in-house subject matter experts have solved the problems/ questions from the exercise with the utmost care and by following all the guidelines by CBSE. Class 6 students who are thorough with all the concepts from the Subject Maths textbook and quite well-versed with all the problems from the exercises given in it, then any student can easily score the highest possible marks in the final exam. With the help of this Class 6 Maths Chapter 5 Exercise 5.5 solutions, students can easily understand the pattern of questions that can be asked in the exam from this chapter and also learn the marks weightage of the chapter. So that they can prepare themselves accordingly for the final exam.

Besides these NCERT solutions for Class 6 Maths Chapter 5 Exercise 5.5, there are plenty of exercises in this chapter which contain innumerable questions as well. All these questions are solved/answered by our in-house subject experts as mentioned earlier. Hence all of these are bound to be of superior quality and anyone can refer to these during the time of exam preparation. In order to score the best possible marks in the class, it is really important to understand all the concepts of the textbooks and solve the problems from the exercises given next to it. 

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