When you look around your environment, do you realise that there are t or objects which are similar in shape but have different sizes?
After studying this chapter and practicing its activities, you should be able to:
demonstrate an understanding of scaling with respect to shape, size and space
construct varying (scaling) sizes of the same shapes to ratio of area or sides
Keywords
area ratio
enlarge
modelling
pole
@ratio
reduce
scale
shapes
side ratio
size
1.1 Introduction
When you look around your environment, do you realise that there are t or objects which are similar in shape but have different sizes? Consider y school uniform, learners wear different sizes. Even when you are at o table, you can use a teaspoon and a tablespoon for different purposes.
A scale is used to make objects with the same shape but with varying s In this chapter, you will understand the concept of scale plotting and make objects of the same shape in varying sizes.
1.2 Enlargement and Reduction by Side
A scale is a ratio whereby the actual size of an object is represented on paper e.g. 11, 21, 1.2 Ratio 1:1 means the actual size of the object is represented on paper. 1:2 means the size of the object is halved on paper while 2:1 means the size of the object is doubled on paper
Enlargement and reduction can be done by prolonging or shortening one side of a given figure. Work out the following examples.
Activity 1.1
Drawing a quadrilateral similar to the one given when its base AB is extended by 17 mm. Use scale 1:1
What you need: 2H pencil, ruler,
pair of compasses, dividers, eraser, T-square, board and clips
What to do: Individually, carry out this activity.
Procedure
Construct a quadrilateral ABCD given that AB=33 mm, AD=40 mm, angle BAD=90°, DC-60 mm and angle ABC-120°. Mark BB,=17 mm.
Draw lines AC and AD and prolong them outwards.
Using a ruler and a set square, draw line B,C, parallel to BC, then draw line D,C, parallel to DC.
Use a sharp pencil to outline the required quadrilateral AB,C,D,.
Activity 1.2
Drawing a quadrilateral similar to the one given when one of its sides AD is reduced by 20 mm. Use scale 1:2
What you need: 2H pencil, ruler, pair of compasses, dividers, eraser, T-square, board and clips
What to do: Individually, carry out
the activity.
Procedure
1.Draw quadrilateral ABCD using
the given dimensions.
Draw lines from A to all the
corners B, C and D. Mark point D, 20 mm from D on line AD.
From D,, draw a line parallel to DC to touch AC at C,. Then from C, draw a line parallel to CB to
touch line AB at B,
1.3 Enlargement and Reduction of Figures Using the Pole
Method (Outside and Inside)
In this method the pole point can be located either inside or outside the given figure. All points of the given figure are connected to this pole point. The ratio of the sides is given. It can be used for either reduction or enlargement of the given figure.
Activity 1.3
Enlarging an irregular pentagon ABCDE using the pole method located outside when the ratio of its sides is 7:5
What you need: 2H pencil, ruler pair of compasses, dividers, eraser T-square board and clips
What to do: Individually carry out this activity. Draw the irregular pentagon in Figure 1.12 and follow the given steps to complete it.
Procedure
Draw the given pentagon using the given information Choose point F at any position outside the pentagon Join Lines from F to all the corners Refer to Figure 1.13
2. Divide FB into 5 equal parts. Extend all lines from F through the corners of pentagon ABCDE
Since it is enlargement, add a distance equal to 2 divisions to Line FB from 8 to get 8, This point 8, will act as a guide to help you obtain C D, E, and A, on the extended Lines. Apply the sliding method to obtain other points C, D, E, and A,
4 Outline the required pentagon as B, C, D, E, A, using a sharp HB pencil
In this method, the pole point can either be positioned inside or outside given figure when enlarging and reducing figures.
Activity 1.4
Reducing a quadrilateral using the pole method located inside when the ratio of its sides is 3:5
What you need: 2H pencil, ruler, pair of compasses, dividers, eraser,
T-square, board and clips
What to do: Individually, draw the irregular pentagon in Figure 1: 16 and follow the given steps to complete it.
Procedure
In pairs, draw the quadrilateral and follow the given steps to complete the task.
Draw the given quadrilateral ABCD given that angle DAB-90° AB-50 mm, BC-40 mm, DC-30 mm and DA=20 mm. 3. Locate the pole point P near Po the middle and draw radiating Lines from P to all the 4 corners A, B, C and D, given ratio of sides =3:5.
Divide PB into 5 equal parts.
From point 3(B), draw line B’C’ parallel to BC Draw a line C’D¹ parallel to CD, draw line D’A’ parallel to DA and finally draw line A’B’ parallel
to AB 6. Join the quadrilateral A’B’C’D’ as the required one with sides in the ratio 3:5
Exercise 1.2
1 Construct the quadrilateral ABCD in Figure 1.17 and show how to reduce it when the ratio of its sides is 2:3, applying the pole point outside the figure.
2 Construct the pentagon ABCDE in Figure 1 18 and demonstrate how to enlarge it when the ratio of its sides is 7:5, applying the pole point inside the given figure.
1.4 Enlargement and Reduction of Different Figures when Given the Ratio of its Area
This is a general method of reducing and enlarging of different figures given the ratio of their area.
Activity 1.5
Reducing an irregular pentagon when given the ratio of its area as 3:5
What you need: 2H pencil, ruler, pair of compasses, dividers, eraser T-square, board and clips
What to do: individually drow the given irregular pentagon and follow the given steps to complete it. Procedure
Using Figure 1.19, construct on Irregular pentagon ABCDE All-40 mm, BC-37 mm, CD-50 mm, DE-56 mm, AE-43 mm. Angle EAB 1200 and angle ABC-90″
2. Extend AB from B and mark 5 equal units of any convenient Length.
3 Draw semicircles on A3 and A5.
4 Draw a perpendicular to AB from B to cut the semicircles at
31 and 51.
5. Join A51 and draw 31A1 parallel to it.
6. Radiate lines B to E and D.
Draw A1E1 parallel to AE. Draw E1D1 parallel to ED. Draw D1C1 parallel to DC to complete the required polygon A1BC1D1.
8. Hence the area of the completed pentagon has been reduced in the ratio 3:5 which is a reduction ABCDE is the given pentagon.
A1BC1 D1E1 is the reduced pentagon.
Activity 1.6
Enlarging an Irregular pentagon when given the ratio of its area as 5:3
What you need: 2H pencil, ruler, pair of compasses, dividers, eraser
T-square board and clips
What to do: In pairs, draw the given irregular pentagon and demonstrate how to enlarge it given the ratio of its areas as 5.3
Procedure
1 Draw an irregular pentagon ABCDE using the same dimensions like in Figure 1.19
2. Extend AB on both directions and mark 5 equal units of any convenient Length from B.
3. Bisect length A3 to get centre O1 and use it to draw semicircle A3
Bisect length A5 to get centre O2 and use it to draw semicircle A5
Drop a perpendicular from B downwards to cut the semicircles at points 31 and
51 respectively. Join 31 to A.
Draw line 51A1 parallel to 31A and touching the extended base at A¹
Draw lines from B through corners E, D and C and extend outwards.
Draw A¹E parallel to AE, draw E1D1 parallel to ED and draw D1C1 parallel to DC to complete the required pentagon A1BC1D1E
Hence the area of this completed pentagon has been enlarged in the ratio 5.3 which is an enlargement.
1.5 Modelling Shapes in Varying Sizes
Activity 1.7
Modelling shapes in varying sizes to represent enlargement and reduction.
What you need: Drawing instruments, paper pins, manilla paper, markers, pair of scissors, knife, blade and cardboard paper
What to do: Individually, carry out this activity.
Draw the following shapes, enlarge or reduce their sizes by their sides or ratios as specified and cut out the shapes for each case.
Enlarge the given parallelogram in Figure 1.24 using the area ratio of 5:3
Reduce the given regular pentagon in Figure 1.25 using the area
ratio of 4:5.
Draw a regular hexagon in a circle of Ø70 mm. Use the pole method inside the hexagon to reduce it when the ratio is 2:3.
Find out any other practical application of enlargement and reduction in your community?
After studying this chapter and practicing its activities, you should be able to:
demonstrate an understanding of scaling with respect to shape, size and space
construct varying (scaling) sizes of the same shapes to ratio of area or sides
Keywords
area ratio
modelling
@ratio
scale
shapes
size
1.1 Introduction
When you look around your environment, do you realise that there are t or objects which are similar in shape but have different sizes? Consider y school uniform, learners wear different sizes. Even when you are at o table, you can use a teaspoon and a tablespoon for different purposes.
A scale is used to make objects with the same shape but with varying s In this chapter, you will understand the concept of scale plotting and make objects of the same shape in varying sizes.
1.2 Enlargement and Reduction by Side
A scale is a ratio whereby the actual size of an object is represented on paper e.g. 11, 21, 1.2 Ratio 1:1 means the actual size of the object is represented on paper. 1:2 means the size of the object is halved on paper while 2:1 means the size of the object is doubled on paper
Enlargement and reduction can be done by prolonging or shortening one side of a given figure. Work out the following examples.
Activity 1.1
Drawing a quadrilateral similar to the one given when its base AB is extended by 17 mm. Use scale 1:1
What you need: 2H pencil, ruler,
pair of compasses, dividers, eraser, T-square, board and clips
What to do: Individually, carry out this activity.
Procedure
Activity 1.2
Drawing a quadrilateral similar to the one given when one of its sides AD is reduced by 20 mm. Use scale 1:2
What you need: 2H pencil, ruler, pair of compasses, dividers, eraser, T-square, board and clips
What to do: Individually, carry out
the activity.
Procedure
1.Draw quadrilateral ABCD using
the given dimensions.
corners B, C and D. Mark point D, 20 mm from D on line AD.
touch line AB at B,
1.3 Enlargement and Reduction of Figures Using the Pole
Method (Outside and Inside)
In this method the pole point can be located either inside or outside the given figure. All points of the given figure are connected to this pole point. The ratio of the sides is given. It can be used for either reduction or enlargement of the given figure.
Activity 1.3
Enlarging an irregular pentagon ABCDE using the pole method located outside when the ratio of its sides is 7:5
What you need: 2H pencil, ruler pair of compasses, dividers, eraser T-square board and clips
What to do: Individually carry out this activity. Draw the irregular pentagon in Figure 1.12 and follow the given steps to complete it.
Procedure
2. Divide FB into 5 equal parts. Extend all lines from F through the corners of pentagon ABCDE
4 Outline the required pentagon as B, C, D, E, A, using a sharp HB pencil
In this method, the pole point can either be positioned inside or outside given figure when enlarging and reducing figures.
Activity 1.4
Reducing a quadrilateral using the pole method located inside when the ratio of its sides is 3:5
What you need: 2H pencil, ruler, pair of compasses, dividers, eraser,
T-square, board and clips
What to do: Individually, draw the irregular pentagon in Figure 1: 16 and follow the given steps to complete it.
Procedure
to AB 6. Join the quadrilateral A’B’C’D’ as the required one with sides in the ratio 3:5
Exercise 1.2
1 Construct the quadrilateral ABCD in Figure 1.17 and show how to reduce it when the ratio of its sides is 2:3, applying the pole point outside the figure.
2 Construct the pentagon ABCDE in Figure 1 18 and demonstrate how to enlarge it when the ratio of its sides is 7:5, applying the pole point inside the given figure.
1.4 Enlargement and Reduction of Different Figures when Given the Ratio of its Area
This is a general method of reducing and enlarging of different figures given the ratio of their area.
Activity 1.5
Reducing an irregular pentagon when given the ratio of its area as 3:5
What you need: 2H pencil, ruler, pair of compasses, dividers, eraser T-square, board and clips
What to do: individually drow the given irregular pentagon and follow the given steps to complete it. Procedure
2. Extend AB from B and mark 5 equal units of any convenient Length.
3 Draw semicircles on A3 and A5.
4 Draw a perpendicular to AB from B to cut the semicircles at
31 and 51.
5. Join A51 and draw 31A1 parallel to it.
6. Radiate lines B to E and D.
8. Hence the area of the completed pentagon has been reduced in the ratio 3:5 which is a reduction ABCDE is the given pentagon.
A1BC1 D1E1 is the reduced pentagon.
Activity 1.6
Enlarging an Irregular pentagon when given the ratio of its area as 5:3
What you need: 2H pencil, ruler, pair of compasses, dividers, eraser
T-square board and clips
What to do: In pairs, draw the given irregular pentagon and demonstrate how to enlarge it given the ratio of its areas as 5.3
Procedure
1 Draw an irregular pentagon ABCDE using the same dimensions like in Figure 1.19
2. Extend AB on both directions and mark 5 equal units of any convenient Length from B.
3. Bisect length A3 to get centre O1 and use it to draw semicircle A3
51 respectively. Join 31 to A.
1.5 Modelling Shapes in Varying Sizes
Activity 1.7
Modelling shapes in varying sizes to represent enlargement and reduction.
What you need: Drawing instruments, paper pins, manilla paper, markers, pair of scissors, knife, blade and cardboard paper
What to do: Individually, carry out this activity.
Draw the following shapes, enlarge or reduce their sizes by their sides or ratios as specified and cut out the shapes for each case.
ratio of 4:5.
Find out any other practical application of enlargement and reduction in your community?
Assignment