Similarity and Congruence
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
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?
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
Scale factor = 5/20 = ¼
x = scale factor x corresponding side
x = ¼ x 12
x = 3
For any triangle
Split the triangles into their components
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
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
Area B = (Scale factor)2 X original area
= 22 X 16
= 4 X 16
= 64 cm2
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
New Volume = (scale factor)3 X original volume
= (1/3)3 X 200
= 1/8 X 200
= 1/8 X 200
= 25 ml
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