Solution of Chapter 4. Basic Geometrical Ideas (NCERT - Mathematics Book)

Chapter Exercises

Exercise 4.1
Exercise 4.2
Exercise 4.3
Exercise 4.4
Exercise 4.5
Exercise 4.6

Exercise 4.1

1

Use the figure to name:


(a) Five points


(b) A line


(c) Four rays


(d) Five-line segments
2

Name the line given in all possible (twelve) ways, choosing only two letters at a time from the four given.
3

Use the figure to name:


(a) Line containing point E.


(b) Line passing through A.


(c) Line on which O lies.


(d) Two pairs of intersecting lines.
4

How many lines can pass through;

(a) one given point?


(b) two given points?
5

Draw a rough figure and label suitably in each of the following cases:

(a) Point P lies on.


(b) and intersect at M.


(c) Line l contains E and F but not D.


(d) and meet at O.
6

Consider the following figure of line . Say whether following statements are true or false in context of the given figure:


(a) Q, M, O, N, and P are the points on the line MN.


(b) M, O, N are points on a line segment MN.


(c) M and N are end points of line segment MN.


(d) O and N are end points of line segment OP.


(e) M is one of the end points of line segment QO.


(f) M is point on ray OP.


(g) is different from .


(h) is same as .


(i) is not opposite to .


(j) O is not an initial point of .


(k) N is the initial point of and

Exercise 4.2

1

Classify the following curves as

(i) Open or


(ii) Closed.
2

Draw rough diagrams to illustrate the following:

(a) Open curve


(b) Closed curve.
3

Draw any polygon and shade its interior.
4

Consider the given figure and answer the questions:

(a) Is it a curve?


(b) Is it closed?
5

Illustrate, if possible, each one of the following with a rough diagram:

(a) A closed curve that is not a polygon.


(b) An open curve made up entirely of line segments.


(c) A polygon with two sides.

Exercise 4.3

1

Name the angles in the given
2

In the given diagram, name the point(s)


(a) In the interior of ∠DOE


(b) In the exterior of ∠EOF.
3

Draw rough diagram of two angles such that they have

(a) One point in common


(b) Two points in common


(c) Three points in common


(d) Four points in common


(e) One ray in common.

Exercise 4.4

1

Draw a rough sketch of a triangle ABC. Mark a point P in its interior and a point Q in its exterior. Is the point A in its exterior or in its interior?
2

Identify three triangles in the figure.
2

Write the names of seven angles.
2

Write the names of six-line segments.
2

Which two triangles have ∠B as common?

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?
2

Draw a rough sketch of a quadrilateral KLMN. State “

(a) two pairs of opposite sides,


(b) two pairs of opposite angles,


(c) two pairs of adjacent sides,


(d) two pairs of adjacent angles.
3

Investigate:

Use strips 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 quadrilaterals?

Exercise 4.6

1

From the figure, identify:


(a) the centre of the circle


(b) three radii


(c) a diameter


(d) a chord


(e) two-points in the interior


(f) a point in the exterior


(g) a sector


(h) a segment
2

Is every diameter of a circle also a chord?
2

Is every chord of a circle also a diameter?
3

Draw any circle and mark

(a) its centre


(b) a radius


(c) a diameter


(d) a sector


(e) a segment


(f) a point in its interior


(g) a point in its exterior


(h) an arc
4

Say true or false:

(a) Two diameters of a circle will necessarily intersect.


(b) The centre of a circle is always in its interior.