Congruent and similar shapes - Maths Part 1

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Similar shapes

Similar figures are identical in shape, but not in size.

For example, two circles are always similar,

Two squares are always similar:

And two rectangles could be similar:

But will probably not be.

Similar figures 

Shape A: Five sided shape, from clockwise directions mesurements from top: 2cm, left-angle: 225 degrees, right-side: 4cm, bottom-left corner: 45 degrees, bottom: 5cm, left-side: 7cm. Shape B: Five sided shape, from clockwise directions lengths from top: 4cm, left-angle: 225 degrees, right-side: 8cm, bottom-left corner: 45 degrees, bottom: 10cm, left-side: 14cm. (http://www.bbc.co.uk/schools/gcsebitesize/maths/images/figure_1.gif)

B is an enlargement of A. The lengths have doubled. but the angles have stayed the same.

Remember: For any part of similar figures corresponding sides are in the same ratio and corresponding angles are equal.

Look at the diagram below. Figures abcd and ABCD are similar.

images: 4 sided shape: left shape: top length: corners BC:4cm, right-side: CD: corners CD: both 90 degree angles, bottom length: DA: 8cm, left-side: at an angle: AB. Right shape: top length: corners BC:6cm, right-side: CD: corners BC:4cm, right-side: CD, corners CD: both 90 degree angles, bottom length: DA: 12cm, left-side: at an angle: AB  (http://www.bbc.co.uk/schools/gcsebitesize/maths/images/figure_2.gif)

ad/AD = 8/12 = 2/3 and bc/BC = 4/6

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effective notes

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