NCERT solutions for Mathematics [English] Class 6 chapter 4 - Basic Geometrical Ideas [Latest edition]

Use the figure to name Five points.

Use the figure to name the A line.

Use the figure to name Four rays.

Use the figure to name Five line segments.

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

Use the figure to name:

Line containing point E.

Use the figure to name:

Line passing through A.

Use the figure to name:

Line on which O lies.

Use the figure to name:

Two pairs of intersecting lines.

How many lines can pass through one given point?

How many lines can pass through two given points?

Draw a rough figure and label it suitably in the following case:

Point P lies on `overline"AB"`.

Draw a rough figure and label it suitably in the following case:

\[\overleftrightarrow{XY}\] and \[\overleftrightarrow{PQ}\] intersect at M.

Draw a rough figure and label it suitably in the following case:

Line l contains E and F but not D.

Draw a rough figure and label it suitably in the following case:

\[\overleftrightarrow{OP}\] and \[\overleftrightarrow{OQ}\] meet at O.

Consider the following figure of line \[\overleftrightarrow{MN}\]. Say whether the following statement is true or false in the context of the given figure.

Q, M, O, N, and P are points on the line \[\overleftrightarrow{MN}\].

Consider the following figure of line \[\overleftrightarrow{MN}\]. Say whether the following statement is true or false in the context of the given figure.

M, O, and N are points on a line segment `overline("MN")`.

Consider the following figure of line \[\overleftrightarrow{MN}\]. Say whether the following statement is true or false in the context of the given figure.

M and N are the end points of line segment `overline"MN"`.

Consider the following figure of line \[\overleftrightarrow{MN}\]. Say whether the following statement is true or false in the context of the given figure.

O and N are end points of line segment `overline"OP"`.

Consider the following figure of line \[\overleftrightarrow{MN}\]. Say whether the following statement is true or false in the context of the given figure.

M is one of the end points of line segment `overline"QO"`.

Consider the following figure of line \[\overleftrightarrow{MN}\]. Say whether the following statement is true or false in the context of the given figure.

M is the point on ray `vec"OP"`.

Consider the following figure of line \[\overleftrightarrow{MN}\]. Say whether the following statement is true or false in the context of the given figure.

Ray `vec("OP")` is different from ray `vec("QP")`.

Consider the following figure of line \[\overleftrightarrow{MN}\]. Say whether the following statement is true or false in the context of the given figure.

Ray `vec("OP")` is the same as ray `vec("OM")`.

Consider the following figure of line \[\overleftrightarrow{MN}\]. Say whether the following statement is true or false in the context of the given figure.

Ray `vec("OM")` is not opposite to ray `vec("OP")`.

Consider the following figure of line \[\overleftrightarrow{MN}\]. Say whether the following statement is true or false in the context of the given figure.

O is not an initial point of `vec("OP")`.

Consider the following figure of line \[\overleftrightarrow{MN}\]. Say whether the following statement is true or false in the context of the given figure.

N is the initial point of `vec("NP")` and `vec("NM")`.

Classify the following curve as Open or Closed.

Classify the following curve as Open or Closed.

Classify the following curve as Open or Closed.

Classify the following curve as Open or Closed.

Classify the following curve as Open or Closed.

Draw a rough diagram to illustrate the following:

Open curve

Draw a rough diagram to illustrate the following:

Closed curve

Draw any polygon and shade it's interior.

Consider the given figure and answer the question:

Is it a curve?

Consider the given figure and answer the question:

Is it closed?

Illustrate, if possible the following with a rough diagram:

A closed curve that is not a polygon.

Illustrate, if possible the following with a rough diagram:

An open curve is made up entirely of line segments.

Illustrate, if possible the following with a rough diagram:

A polygon with two sides.

Name the angles in the given figure.

In the given diagram, name the point.

In the interior of ∠DOE

In the given diagram, name the point.

In the exterior of ∠EOF

In the given diagram, name the point.

On ∠EOF

Draw a rough diagram of two angles such that they have One point in common.

Draw a rough diagram of two angles such that they have Two points in common.

Draw a rough diagram of two angles such that they have Three points in common.

Draw a rough diagram of two angles such that they have Four points in common.

Draw a rough diagram of two angles such that they have One ray in common.

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

Identify three triangles in the figure.

Write the names of seven angles.

Write the names of six line segments.

Which two triangles have ∠B in common?

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?

Draw a rough sketch of a quadrilateral KLMN. State two pairs of opposite sides.

Draw a rough sketch of a quadrilateral KLMN. State two pairs of opposite angles.

Draw a rough sketch of a quadrilateral KLMN. State two pairs of adjacent sides.

Draw a rough sketch of a quadrilateral KLMN. State two pairs of adjacent angles.

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?

From the figure, identify the centre of the circle.

From the figure, identify three radii.

From the figure, identify a diameter.

From the figure, identify a chord.

From the figure, identify two points in the interior.

From the figure, identify a point in the exterior.

From the figure, identify a sector.

From the figure, identify a segment.

Is every diameter of a circle also a chord?

Is every chord of a circle also a diameter?

Draw any circle and mark

1. it's centre
2. a radius
3. a diameter
4. a sector
5. a segment
6. a point in its interior
7. a point in its exterior
8. an arc

Say true or false:

Two diameters of a circle will necessarily intersect.

Say true or false:

The centre of a circle is always in its interior.