R d sharma mathematics solutions class 6 Solutions for Chapter 10 basic geometrical concepts

Make three points in your notebook and name them.

Draw a line in your notebook and name it using a small letter of the alphabet.

Draw a line in your notebook and name it by taking any two points on it.

Give three examples from your environment of:

(i) Points

(ii) Portion of a line

(iii) Plane surfaces

(iv) Portion of a plane

(v) Curved surfaces

There are a number of ways by which we can visualise a portion of a line. State whether the following represent a portion of a line or not:

(i) A piece of elastic stretched to the breaking point.

(ii) Wire between two electric poles.

(iii) The line thread by which a spider lowers itself.

Can you draw a line on the surface of a sphere which lies wholly on it?

Mark a point on a sheet of paper and draw a line passing through it. How many lines can youdraw through this point?

Mark any two points P and Q in your note book and draw a line passing through the points. How many lines can you draw passing through both the points?

Give an example of a horizontal plane and a vertical plane from your environment.

How many lines may pass through one given point, two given points, any three collinear points?

Is it ever possible for exactly one line to pass through three points?

Explain why it is not possible for a line to have a mid-point.

Mark three non-collinear points A, B and C in your note book. Draw lines through these points taking two at a time. Name these lines. How many such different lines can be drawn?

Coplanar points are the points that are in the same plane. Thus, (i) Can 150 points be coplanar? (ii) Can 3 points be non-coplanar?

Using a ruler, check whether the following points given in Fig. 10.30 are collinear or not:

(i) D, A and C

(ii) A, B and C

(iii) A, B and E

(iv) B, C and E

Using a ruler, check whether the following points given in Fig. 10.30 are collinear or not:

(i) D, A and C

(ii) A, B and C

(iii) A, B and E

(iv) B, C and E

Give three examples each of:

(i) intersecting lines

(ii) parallel lines from your environment.

From Fig. 10.21, write

(i) all pairs of parallel lines.

(ii) all pairs of intersecting lines.

(iii) lines whose point of intersection is I.

(iv) lines whose point of intersection is D.

(v) lines whose point of intersection is E.

(vi) lines whose point of intersection is A.

(vii) collinear points.

From Fig. 10.22, write concurrent lines and their points of concurrence.

Mark four points A, B, C and D in your notebook such that no three of them are collinear. Draw allthe lines which join them in pairs as shown in Fig. 10.23.

(i) How many such lines can be drawn?

(ii) Write the names of these lines.

(iii) Name the lines which are concurrent at A.

What is the maximum number of points of intersection of three lines in a plane? What is the minimum number?

With the help of a figure, find the maximum and minimum number of points of intersection offour lines in a plane.

Lines p, q and r are concurrent. Also, lines p, r and s are concurrent. Draw a figure and statewhether lines p, q, r and s are concurrent or not.

Lines p, q and r are concurrent. Also lines p, s and t are concurrent. Is it always true that the lines q, r and s will be concurrent? Is it always true for lines q, r and t?

Fill in the blanks in the following statements using suitable words:

(i) A page of a book is a physical example of a ….

(ii) An inkpot has both ……. Surfaces

(iii) Two lines in a plane are either ……. or are ….

State which of the following statements are true (T) and which are false (F):

(i) Point has a size because we can see it as a thick dot on paper.

(ii) By lines in geometry, we mean only straight lines.

(iii) Two lines in a plane always intersect in a point.

(iv) Any plane through a vertical line is vertical.

(v) Any plane through a horizontal line is horizontal.

(vi) There cannot be a horizontal line in a vertical plane.

(vii) All lines in a horizontal plane are horizontal.

(viii) Two lines in a plane always intersect in a point.

(ix) If two lines intersect at a point P, then P is called the point of concurrence of the two lines.

(x) If two lines intersect at a point P, then P is called the point of intersection of the two lines.

(xi) If A, B, C and D are collinear points D, P and Q are collinear, then points A, B, C, D, P and Q are always collinear.

(xii) Two different lines can be drawn passing through two given points.

(xiii) Through a given point only one line can be drawn.

(xiv) Four points are collinear if any three of them lie on the same line.

(xv) The maximum number of points of intersection of three lines is three.

(xvi) The maximum number of points of intersection of three lines is one.

Give the correct matching of the statements of Column A and Column B.

In Fig. 10.32, points are given in two rows. Join the points AM, HE, TO, RUN, IF. How many line segments are formed?

In Fig. 10.33, name:

(i) Five line segments

(ii) Five rays

(iii) Non-intersecting line segments

In each of the following cases, state whether you can draw line segments on the given surfaces:

(i) The face of a cuboid.

(ii) The surface of an egg or apple.

(iii) The curved surface of a cylinder.

(iv) The curved surface of a cone.

(v) The base of a cone.

Mark the following points on a sheet of paper. Tell how many line segments can be obtained in each case:

i) Two points A, B. (ii) Three non-collinear points A, B, C.

(iii) Four points such that no three of them belong to the same line.

(iv) Any five points so that no three of them are collinear.

Count the number of a line segments in Fig. 10.34.

In Fig. 10.35, name all rays with initial points as A, B and C respectively.

Give three examples of line segments from your environment.

Draw rough diagrams to illustrate the following:

(i) Open curve

(ii) Closed curve

Classify the following curves as open or closed:

Draw a polygon and shade its interior. Also draw its diagonals, if any.

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

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

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

(iii) A polygon with two sides.