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**Congruence and Similarity**

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Similar Two shapes are similar if their corresponding angles are equal and their corresponding sides are in proportion.

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**Bottom Length 10 cm Top Length 3 cm**

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Congruent Two shapes are congruent if all corresponding angles AND sides are equal. If two shapes are congruent, they are also similar.

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Top Length 4 cm Bottom Length 5 cm

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Perimeter To find the perimeter of any polygon, add up the length of all sides.

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**Triangles Triangles have 3 angles that add up to 180 degrees.**

To find the area of a triangle, multiply ½ the base x the height.

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**Rectangles Rectangles have 4 right angles that add up to 360 degrees.**

To find the area of a rectangle, multiply the length x the width.

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Scale Factor The ratio of corresponding side lengths of two similar figures. All congruent shapes have a scale factor of 1:1.

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**B A The scale factor from A to B is 5:2.**

Length = 10 cm Width = 5 cm The scale factor from A to B is 5:2. The ratio of areas from A to B is 25:4 Length = 4 cm Width = 2 cm B

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Missing Side You can find the missing side length on one of two similar figures by using a proportion involving scale factor.

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**B A Set up a proportion. Cross multiply and divide. 20 = 5 4 x**

A and B are similar. A Length = 20 cm Width = 5 cm Set up a proportion. Cross multiply and divide. = x So, x = 1 cm B Length = 4 cm Width = ? cm

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Missing Angle You can find the measure of a missing angle on one of two similar triangles by subtracting from 180 degrees.

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**If triangles xyz and def are similar, what is the measure of angle y?**

500 y z d Y = 60 degrees because = 120. 180 – 120 = 60. e f 700

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