Passnownow

Rated 4.8/5 by parents & students

Classwork Exercise and Series (Mathematics-JSS3): Similarity And Enlargement

Similarity and Congruence

1

Two objects are similar if they have the same shape, so that one is an enlargement of the other.

Two objects are congruent if they are the same shape and size.

Corresponding angles are equal. Corresponding lengths are in the same ratio – they have the same Scale Factor. The scale factor is greater than 1 for an enlargement. The scale factor is smaller than 1 for a reduction.

Example

a c

2
3:2 or 1.5 or 3/2

Two shapes are said to be similar if one is a scaled version of the other. This means that their corresponding angles are equal; their corresponding sides are in the same ratio. (ie. they have the same scale factor) similar?

dom

Check that their corresponding angles are equal. Check the ratio of their corresponding sides.

Length of A/Length of B

= 20 mm/30 mm

= 2/3

Breadth of A/Breadth of B

10 mm/15 mm

2/3

x = scale factor x corresponding side

4

Scale factor = 5/20 = ¼

x = scale factor x corresponding side

x = ¼ x 12

x = 3

For any triangle
sim

Split the triangles into their components

1

2

x = scale factor X corresponding side

scale factor = AB/AD = 12/15 = 4/5

corresponding side = DE = 10 cm

x = 4/5 X 10

x = 40/5 = 8 cm

x = scale factor X corresponding side

12

Area A = 6 cm2

Scale factor = 2

(Scale factor)2  = 4

Area B = 24 cm2

Area B = 4 X 6

= 4 X Area A

Area B = (Scale factor)2  X original area

Scaled area = (Scale factor)2  X original area

12

112

Area B = (Scale factor)2  X original area

= 22 X 16

                 = 4 X 16

= 64 cm2

simvol

 

Area A = 6cm2

Volume A = 6 cm2

(Scale factor)2  = 8

Area B = 24 cm2

Volume B = 48cm3

Volume B = 8 X 6 = 8 X Volume A

Scale Volume = (Scale factor)3 x original volume

pongo

New Volume = (scale factor)3 X original volume

= (1/3)3 X 200

= 1/8 X 200

= 1/8 X 200

= 25 ml

For more notes; see: http://passnownow.com/classwork-support/

 

 

Leave a Comment

Your email address will not be published. Required fields are marked *

Scroll to Top