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| Summary |
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 Enlargement or Dilatation |
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If
DPQR is the image of DABC (Pre image) and K is the enlargement factor,  |
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If K = 1 the triangles are congruent. |
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The ratio of their areas is K2 |
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(SAS similarity) |
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| If a pair of corresponding angles are equal and the sides including them are proportional, the triangles are similar. |
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(AA similarity) |
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| If two pairs of corresponding angles are equal then the triangles are similar |
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(SSS similarity) |
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| If three pairs of corresponding sides are proportional, then the two triangles are similar. |
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A perpendicular drawn from the right angle vertex of a right triangle to the hypotenuse divides the triangle into two triangles similar to each other and also to the original triangle. |
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In
DABC, if ÐA = 90o and
AD ^ BC (D is the foot of the altitude) |
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| AB2 = BC . BD, AC2 = BC . CD and AD2 = BD.CD |
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