NCERT Solutions for Class 6 Maths Chapter 4: Basic Geometrical Ideas - Exercise 4.5

Exercise 4.5

1. Draw a rough sketch of a quadrilateral $PQRS$. Draw its diagonals. Name them. Is the meeting point of the diagonals in the interior or exterior of the quadrilateral?

Ans: A four sided polygon with four edges is known as a quadrilateral.

Draw a quadrilateral $PQRS$ using a geometry tool.

To draw diagonals of the quadrilateral $PQRS$ join edges $P$, $R$ and $Q$, $S$. Label the point where both the diagonals intersect. Diagonals of the quadrilateral $PQRS$ are $\overline {PR} $ and $\overline {SQ} $.

From the above figure it is seen that the intersection point of two diagonals, that is $O$, is inside the quadrilateral. Thus the point where two diagonals meet is in the interior of the quadrilateral.

2. Draw a rough sketch of a quadrilateral $KLMN$. State:

a) Two pairs of opposite sides.

Ans: A four sided polygon with four edges is known as a quadrilateral.

Draw a quadrilateral $KLMN$ using a geometry tool.

Opposite sides of the quadrilateral are the sides that do not have a common endpoint.

From the figure it is seen that opposite sides of the quadrilateral are $KL$ and $NM$, $KN$ and $LM$.

b) Two pairs of opposite angles.

Ans: A four sided polygon with four edges is known as a quadrilateral.

Draw a quadrilateral $KLMN$ using a geometry tool.

From the figure it is seen that a pair of opposite angles of a quadrilateral are $\angle K$ and $\angle M$, $\angle L$ and $\angle M$.

c) Two pairs of adjacent sides.

Ans: A four sided polygon with four edges is known as a quadrilateral.

Draw a quadrilateral $KLMN$ using a geometry tool.

Adjacent sides of the quadrilateral are the sides that have a common endpoint.

From the figure it is seen that adjacent sides of the quadrilateral are $KL$ and $LM$, $KN$ and $NM$.

d) Two pairs of adjacent angles.

Ans: A four sided polygon with four edges is known as a quadrilateral.

Draw a quadrilateral $KLMN$ using a geometry tool.

If two angles of a quadrilateral share a common side then the angles are called adjacent angles of a quadrilateral.

From the figure it is seen that a pair of adjacent angles of quadrilateral are $\angle K$ and $\angle L$, $\angle M$ and $\angle N$.

3. Investigate: Use strip and fasteners to make a triangle and a quadrilateral. Try to push inward at any one vertex of the triangle. Do the same to the quadrilateral. Is the triangle distorted? Is the quadrilateral distorted? Is the triangle rigid? Why is it that structures like electric towers make use of triangular shapes and not quadrilateral?

Ans: Make a triangle using strips and fasteners.

Push one vertex inward and see the change in the shape.

On pushing one vertex inward the whole triangle moves and thus the shape remains unchanged. Therefore the triangle is not distorted and is rigid.

Make a quadrilateral using strips and fasteners.

Push one vertex inward and see the change in the shape.

On pushing one vertex the inward shape of the quadrilateral is distorted.

Since on moving the ends of triangle shape remains unchanged thus electric towers use triangular shape rather than a quadrilateral.

NCERT Solutions for Class 6 Maths Chapter 4 Basic Geometrical Ideas Exercise 4.5

Opting for the NCERT solutions for Ex 4.5 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 4.5 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 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 4 Exercise 4.5 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 4 Exercise 4.5, 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. 

Do not delay any more. Download the NCERT solutions for Class 6 Maths Chapter 4 Exercise 4.5 from Vedantu website now for better exam preparation. If you have the Vedantu app in your phone, you can download the same through the app as well. The best part of these solutions is these can be accessed both online and offline as well.