Selina solutions for Mathematics [English] Class 6 chapter 23 - Fundamental Concepts geometry [Latest edition]

State, true or false, if false, correct the statement.

A dot has width but no length.

State, true or false, if false, correct the statement.

A ray has an infinite length only on one side of it.

State, true or false, if false, correct the statement.

A line segment PQ is written as \[\overleftrightarrow{PQ}\]

State, true or false, if false, correct the statement.

\[\overleftrightarrow{PQ}\] represents a straight line.

State, true or false, if false, correct the statement.

Three points are said to be collinear, if they lie in the same plane.

State, true or false, if false, correct the statement.

Three or more points all lying in the same line, are called collinear points.

Write how many line can be drawn through a given point?

Write how many line can be drawn through two given fixed points?

Write how many line can be drawn through three collinear points?

Write how many line can be drawn through three non-collinear points?

The shaded region of the given figure shows a plane:

(i) Name the three collinear points.

(ii) Name the three non-collinear points.

(iii) Name a pair of intersecting lines.

The shaded region of the given figure shows a plane:

State whether true or false of the following statement:

(i) Line DE is contained in the given plane P.
(ii) Lines AB and DE intersect at point C.
(iii) Points D, B and C are collinear.
(iv) Points D, B and E are collinear.

Correct the statement, if it is wrong:

A ray can be extended infinitely on either side.

Correct the statement, if it is wrong:

A ray has a definite length.

Correct the statement, if it is wrong:

A line segment has a definite length.

Correct the statement, if it is wrong:

A line has two end-points.

Correct the statement, if it is wrong:

A ray has only one end point.

State true or false, if false give the correct statement:

A line has a countable number of points in it.

State true or false, if false give the correct statement:

Only one line can pass through a given point.

State true or false, if false give the correct statement:

The intersection of two planes is a straight line

State, whether the following pair of line or ray appear to be parallel or intersecting.

State, whether the following pair of line or ray appear to be parallel or intersecting.

State, whether the following pair of line or ray appear to be parallel or intersecting.

State, whether the following pair of line or ray appear to be parallel or intersecting.

Give two examples, from your surrounding, for the following: 

points

Give two examples, from your surrounding, for the following: 

line segments

Give two examples, from your surrounding, for the following: 

plane surfaces

Give two examples, from your surrounding, for the following: 

curved surfaces

Under what condition will two straight lines, in the same plane, have no point in common.

If possible draw a diagram in support of your answer.

Under what condition will two straight lines, in the same plane, have only one point in common. 
If possible draw a diagram in support of your answer.

Under what condition will two straight lines, in the same plane, have: an infinite number of points in common.
If possible draw a diagram in support of your answer.

Mark two points A and B on a page of your exercise book. Mark a third point P, such that:

P lies between A and B ; and the three points A, P and B are collinear.

Mark two points A and B on a page of your exercise book. Mark a third point P, such that:

P does not lie between A and B yet the three points are collinear.

Mark two points A and B on a page of your exercise book. Mark a third point P, such that:

the three points do not lie in a line.

Mark two points P and Q on a piece of paper. How many lines can you draw the passing through both the points P and Q?

Mark two points P and Q on a piece of paper. How many lines can you draw the passing through point P?

Mark two points P and Q on a piece of paper. How many lines can you draw the passing through the point Q?

The adjoining diagram shows a line AB. Draw diagram to represent: ray AB i.e. \[\underrightarrow{AB}\]

The adjoining diagram shows a line AB. Draw diagram to represent:  \[\underrightarrow{BA}\]

The adjoining diagram shows a line AB. Draw diagram to represent: line segment AB.

The adjoining diagram shows a ray AB. Draw diagrams to show the ray BA i.e. \[\underrightarrow{BA}\]

The adjoining diagram shows a ray AB. Draw diagrams to show the line AB.

The adjoining diagram shows a ray AB. Draw diagrams to show the line segment BA.

The adjoining diagram shows a line segment AB. Draw diagrams to represent the ray AB i.e. \[\underrightarrow{AB}\]

The adjoining diagram shows a ray AB. Draw diagrams to show the line AB i.e. \[\underleftrightarrow{AB}\].

The adjoining diagram shows a line segment AB. Draw diagrams to represent the ray BA.

Use a ruler and whether the following points are collinear or not:

D, A and C

Use a ruler and whether following points are collinear or not:

A, B and C

Use a ruler and whether following points are collinear or not:

A, B and E

Use a ruler and whether following points are collinear or not:

B, C and E

From the adjoining figure, write: all pairs of parallel lines.

From the adjoining figure, write: all the lines which intersect EF.

From the adjoining figure, write: lines whose point of intersection is G. 

State if the following is a plane closed figure:

State if the following is a plane closed figure:

State if the following is a plane closed figure:

State if the following is a plane closed figure:

State if the following is a plane closed figure:

State if the following is a plane closed figure:

State if the following is a plane closed figure:

State if the following is a plane closed figure:

Fill in the blank:

______ is a three sided plane closed figure.

Fill in the blank:

A square is a plane closed figure which is not bounded by _______.

Fill in the blank:

A rectangle is a _____ sided plane _______.

Fill in the blank:

A rectangle has opposite sides ______ and adjacent sides ________ to each other.

Fill in the blank:

The sides of a square are ______ to each other and each angle is ____.

Fill in the blank:

For a line segment, a line making the angle of ______ with it, is called perpendicular to it.

Fill in the blank:

For a line segment, a line ______ it and making angle of ______ with it, is called ______ bisector of the line segment.

Fill in the blank:

How many perpendiculars can be drawn to a line segment of length 6 cm?

Fill in the blank:

How many perpendicular bisectors can be drawn to a line segment of length 6 cm?

Fill in the blank:

A perpendicular to a line segment will be its perpendicular bisector if it passes through the _______ of the given line segment.

State, which of the lines/line- segments are perpendicular to the line PQ:

State if the following figure shows two mutually perpendicular lines:

State if the following figure shows two mutually perpendicular lines:

State if the following figure shows two mutually perpendicular lines:

The figure is given below name the line segment that is a perpendicular bisector of the other:

The figure is given below name the line segment that is a perpendicular bisector of the other:

The figure is given below name the line segment that is a perpendicular bisector of the other:

The figure is given below name the line segment that is a perpendicular bisector of the other:

The figure is given below name the line segment that is a perpendicular bisector of the other:

Name three objects from your surroundings that contain perpendicular edges.

Using the given figure, answer the following:

Name the pairs of parallel lines.

Using the given figure, answer the following:

Name the pairs of mutually perpendicular lines.

Using the given figure, answer the following:

Is the line p parallel to the line l?

Using the given figure, answer the following:

Is the line q perpendicular to the line m?

Place a scale (ruler) on a sheet of paper and hold it firmly with one hand. Now draw two line segments AB and CD along the longer edges of the scale. State whether segment AB is parallel to or perpendicular to segment CD.

Check your text book and How many pairs of its edges are parallel to each other ?

Check your text book and How many pairs of its edges are perpendicular to each other?

Give two examples from your surrounding for the following:

intersecting lines

Give two examples from your surrounding for the following:

parallel lines

Give two examples from your surrounding for the following:

perpendicular lines

State true or false; if false, give the correct statement:

The maximum number of lines through three collinear points is three.

State true or false; if false, give the correct statement:

The maximum number of lines through three non-collinear points is three.

State true or false; if false, give the correct statement:

Two parallel lines always lie in the same plane.

State true or false; if false, give the correct statement:

Concurrent lines always meet at the same point.

State true or false; if false, give the correct statement:

A surface can be plane or curved.

State true or false; if false, give the correct statement:

There are an infinite number of points in a line segment of length 10 cm.

State true or false; if false, give the correct statement:

There are an infinite number of points in a line.

State true or false; if false, give the correct statement:

A plane has an infinite number of lines.

State true or false; if false, give the correct statement:

A plane has an infinite number of points.

Mark a point O on a piece of paper. Using a sharp pencil and a ruler, draw a line through the point O. Then draw one more line through the point O. How many lines can you draw through O?
Write a statement regarding your observations.

Mark two points A and B on a plain sheet “ of paper. Using a sharp pencil and a ruler, draw a line through points A and B. Try to draw one more line through A and B. What do you observe?
Write a statement regarding your observations.

Draw two straight lines on a sheet of paper so that the lines drawn the intersect each other.

Draw two straight lines on a sheet of paper so that the lines drawn do not intersect.

Draw two straight lines on a sheet of paper so that the lines drawn appear to intersect when extended.

Draw a figure to show that: points A, B and C arc collinear.

Draw a figure to show that: lines AB, CD and EF are concurrent.

In your note-book, draw two rays with the same initial point O and going in opposite directions. Write the special name for the final figure obtained.

In figure is given below, write the number of line segments used:

In figure is given below, write the number of line segments used:

In figure is given below, write the number of line segments used:

In figure is given below, write the number of line segments used:

In a circle, point P is its centre and PA = PB = radius of the circle. Where do points A and B lie?

Draw a four-sided closed figure, in which all the sides are equal and each angle is 90° and also give the special name of the figure drawn.

Draw a four-sided closed figure, in which opposite sides are equal and each angle is 90° and also give the special name of the figure drawn.