WBBSE Notes For Class 6 Maths Geometry Chapter 5 Drawing Of Different Geometrical Figures

Geometry Chapter 5 Drawing Of Different Geometrical Figures

Geometry Chapter 5 To draw a perpendicular line to a given line at a point on it:

1. Method 1. (paper folding process):

Drawing process:

 

 

1. Draw a line segment AB on tracing paper.
2. Take point O on segment AB.
3. Now folds the paper along point O such that the line segments OB coincides with OA.
4. Then open the folding and draw vertical line segments OB folding line.
5. The line segment PQ is the required perpendicular line segment at O on AB.

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Method – 2 (With the help of scale and set square):

Drawing Process:

1. Draw a straight line PQ with the help of scale and take a point A on PQ as shown in the.
2. A scale is placed on PQ such that one edge of the scale coincides with PQ.
3. Now a set square is placed on the scale such that the right-angled point of the set square coincides with point A.
4. Then draw a line segment AB at point A along the vertical side of the set square.
5. AB is the required perpendicular at A on PQ
6. i.e., \(\overline{\mathrm{AB}}\) ⊥ \(\stackrel{\leftrightarrow}{\mathbf{P Q}}\)

 

 

Method – 3. (with the help of scale and pencil compass)

This can be done in 3 ways as described and drawn below

Process 1:

Drawing process:

1. Draw a straight line PQ with the help of a scale and take a point A on it.
2. With the help of a pencil compass, draw a circular arc taking any radius centered at A, so that the arc intersects the line PQ at points C and D.
3. Now with the centers at G and D taking any radius greater than CA on the same side of the straight line PQ, draw two arcs and let them meet at point B.
4. Join points A and B with the help of a scale.
5. AB is the required perpendicular at A on PQ.

 

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Process 2:

Drawing Process :

1. Draw a straight line PQ with the help of a scale and take a point A on PQ.
2. With the help of a pencil compass, draw a circular arc taking any radius centered at A so that the arc intersects the straight line PQ at points E and F.
3. Now with the center at F taking the same radius as before, draw an arc that intersects the previous arc at C.
4. With the center at C and taking the same radius draw an arc that intersects the previous arc at point D.
5. Now with the center at D and taking the same radius, draw an arc with the help of a pencil compass and let this arc intersects the arc drawn with the center at C at point B as shown in the.
6. Join points A and B with the help of a scale and produce the joining line to M as shown in the.
7. AB is the required perpendicular line to PQ.
8. \(\overline{\mathrm{AM}}\) ⊥ \(\stackrel{\leftrightarrow}{\mathbf{P Q}}\)

 

Class 6 Math Solution WBBSE In English

Process 3:

Drawing Process:

1. Draw a straight line PQ with the help of a scale and take a point on PQ.
2. Take point C outside the straight line PQ.
3. With the center at C and taking the radius CA, draw a semi-circular arc that intersects the straight line PQ at points A and D respectively.
4. With the help of a scale, join D and C and produce DC which intersects the semicircular arc at B as shown in the.
5. With the help of a scale, join A and B.
6. AB is the required perpendicular line to PQ.
7. i.e., \(\overline{\mathrm{AB}}\) ⊥ \(\stackrel{\leftrightarrow}{\mathbf{P Q}}\)

 

 

Geometry Chapter 5 Draw a perpendicular line to a given line from a point lying outside the given line

Class 6 Math Solutions WBBSE English Medium

Method – 1 (Paper folding process):

Drawing Process:

1. Take a rectangular tracing paper.
2. Draw a straight line AB on this paper and take point O outside the straight line AB.
3.  Now fold the paper along point O such that the mark of folding the paper will lie on both sides of line AB and the straight line on both sides of the folding should coincide.
4. Now open the folding and draw a straight line along the mark of folding by a scale so that this drawing straight line intersects AB at M.
5. OM is the required perpendicular straight line to AB
6. i.e., \(\overline{\mathrm{OM}}\) ⊥ \(\stackrel{\leftrightarrow}{\mathbf{A B}}\)

 

 

 

Method – 2 (with the help of scale and pencil compass):

There are 2 processes that are described and drawn below:

 

Class 6 Math Solutions WBBSE English Medium

Process 1:

Drawing Process :

1. With the help of a scale, draw a straight line AB and take a point O outside the line AB.
2. Take a point P on that side of the straight line AB opposite to that of O.
3. With the help of a pencil compass, taking a radius equal to OP and centered at O, draw a circular arc that intersects AB at points C and D respectively.
4. With the center at C and D, taking the radius greater than half of the length CD draw two arcs on the side of AB where the point P lies.
5. Let these two arcs intersect at N.
6. Join the points O and N with the scale and let this straight line ON intersect AB at M.
7. OM is the required perpendicular from O on AB
8. i.e. \(\overline{\mathrm{OM}}\) ⊥ \(\stackrel{\leftrightarrow}{\mathbf{A B}}\)

 

Process – 2:

Drawing process :

1. With the help of a scale, draw a line AB and take a point O outside the straight line AB.
2. We take any two points C and D on the straight line AB.
3. With the center at C and taking the radius equal to CO, draw a circular arc.
4. With the center at D and taking the radius equal to DO, draw another circular arc that intersects the previous arc at point P.
5. Obviously, these two arcs will intersect at O also.
6. Now join the points O and P with the scale.
7. Let the line segment OP intersect AB at point M.
8. OM is the required perpendicular on AB.
9. i.e., \(\overline{\mathrm{OM}}\) ⊥ \(\stackrel{\leftrightarrow}{\mathbf{A B}}\).

 

 

Class 6 Math Solutions WBBSE English Medium

Method – 3 (with the help of scale and set square):

Drawing Process :

1. With the help of a scale, draw the straight line AB and take a point O outside the line AB. ,
2. Place any side other than the hypotenuse of the set square such that this side coincides with AB.
3. Now place a scale along the hypotenuse of the set square so that the edge of the scale coincides with the hypotenuse of the set square.
4. Now press the scale strongly and ascend the set square and move if necessary so that the vertical edge of the set square coincides with point O.
5. In this position, mark point M where the vertical edge of the set square intersects the line AB as shown in the.
6. Now join O and M.
7. OM is the required perpendicular on the straight line AB.
8. i.e., \(\overline{\mathrm{OM}}\) ⊥ \(\stackrel{\leftrightarrow}{\mathbf{A B}}\).

 

 

Geometry Chapter 5 Perpendicular-bisector

Definition:

1. The perpendicular upon a line segment at its mid-point is called the perpendicular bisector of the line segment.
2. In the above AB is a line segment and P is its mid-point.
3. OP is perpendicular to the line segment AB at P.
4. OP is called the perpendicular bisector, of AB.
5. So a perpendicular bisector is
   1. Perpendicular to the given line segment.
   2. It divides the given line segment into equal parts i.e., a perpendicular bisector upon a line segment bisects the given line segment.
6. Now we shall discuss how to draw a perpendicular bisector to a given line segment.

 

Class 6 Math Solutions WBBSE English Medium

Geometry Chapter 5 Draw the perpendicular bisector of a given line segment

The different methods of drawing the perpendicular bisector upon a given line segment are discussed below:

Method – 1 (Paper folding process):

Drawing process:

1. We take a rectangular piece of paper and fold the paper along a horizontal line.
2. Then open the folding (in along the CD).
3. Along the folding, draw a line segment AB.
4. Now the paper is folded vertically (in the along EF) such that point A completely falls D on point B.
5. Now, open the folding paper and draw a line segment OP along the vertical folding and it intersects the line segment AB at point P.
6. ∴ OP is the required perpendicular bisector of the line segment AB.

 

Method – 2 (with the help of scale and pencil compass):

Drawing Process:

1. At first, we draw a line segment AB with the help of scale.
2. With the centers at A and B respectively, taking the
3. radius equal to the length AB, we draw two circular arcs with help of a pencil compass.
4. Let the arcs intersect each other at points O and Q.
5. Join the points O and Q with a scale.
6. Let this line segment OQ intersect AB at P.
7. OP is the required perpendicular bisector of the line segment AB.

 

Class 6 Math Solution WBBSE

Method – 3 (with the help of scale and pencil compass):

Drawing Process:

1. With the help of a scale, draw a line segment AB.
2. With the center at point A, taking the radius greater than, half of AB, draw two arcs, one arc on each side of the line segment AB.
3. With the center at point B, taking the same radius, draw two arcs, one arc on each side of the line segment AB.
4. Let these arcs intersect the previous arcs at points O and Q respectively.
5. With the help of a scale, join O and Q.
6. Let the line segment OQ intersect the line segment AB at P.
7. OP is the required perpendicular bisector of the line segment AB.

 

 

Geometry Chapter 5 To Draw an angle that is equal to a given angle

Let ∠AOB be a given angle. We have to draw an angle that is equal to ∠AOB.

Drawing Process:

1. With the help of a scale, a line segment QR be drawn.
2. With the center O of the angle AOB and taking any radius.
3. We draw a circular arc that intersects the side OA at C and the side OB at D.
4. Now with the center at Q of the line segment QR and taking a radius equal to \(\overline{\mathrm{OC}}\) or \(\overline{\mathrm{OD}}\) draw a circular arc that intersects the line segment QR at E.
5. Now, with the center at E and taking the radius \(\overline{\mathrm{CD}}\), draw another circular arc that intersects the previous arc with the center at Q at F.
6. Join the points Q and F by a scale and produce QF to point P.
7. Then ∠PQR is the required angle.
8. ∴ ∠PQR = AOB.

Class 6 Math Solution WBBSE

Geometry Chapter 5 To bisect a given angle (with the help of a scale and a pencil compass)

Let ∠AOB be a given angle. We have to bisect it.

 

 

Drawing Procedure:

1. First, with the center at O of the ∠AOB and taking the radius, draw a circular arc.
2. Let this arc intersect the side OA and the side OB of the angle ∠AOB at points C and D respectively.
3. Now with the centers at points C and D and taking the radius equal to CD (or greater than half of CD) within the angle ∠AOB, we draw consecutively two arcs.
4. Let these two arcs intersect each other at point Q.
5. Join the points O and Q by a scale and produce OQ to point P.
6. Then OP is the required bisector i.e. OP is the bisector of the ∠AOB
7. ∴ ∠AOP = ∠BOP.