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16 Cards in this Set
- Front
- Back
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Ratio
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The ratio of 'a' to 'b' can be written as the fraction a/b.
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Proportion
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An equality between two ratios.
a/b = c/d (This is a fraction set equal to another fraction.) |
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Geometric mean
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The number 'a' is the geometric mean between the numbers 'a' and 'c' if 'a', 'b', and 'c' are positive and
a/b = b/c |
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Similar, similarity
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(Informal definition) Same shape, different size. Angle measure will be equal, but side lengths are proportional.
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Similar triangles
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Two triangles are similar iff there is a correspondence between their vertices such that their corresponding sides are proportional and their corresponding angles are equal.
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Side-Splitter Theorem
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If a line parallel to one side of a triangle intersects the other two sides in different points, it divides the sides in the same ratio.
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Corollary to the Side-Splitter Theorem
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If a line parallel to one side of a triangle intersects the other two sides in different points, it cuts off segments proportional to the sides.
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The AA Theorem
(Triangle Similarity) |
If two angles of one triangle are equal to two angles of another triangle, the triangles are similar.
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Corollary to the AA Theorem
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Two triangles similar to a third triangle are similar to each other.
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Corresponding Altitudes Theorem
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Corresponding altitudes of similar triangles have the same ratio as that of the corresponding sides.
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Ratio of Perimeters Theorem
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The ratio of the perimeters of two similar polygons is equal to the ratio of the corresponding sides.
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Ratio of Areas Theorem
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The ratio of the areas of two similar polygons is equal to the square of the ratio of the corresonding sides.
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Center of dilation
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If two similar items are aligned so that sides are parallel, then straight lines drawn from corresponding vertices will intersect in a point, which can be called the center of dilation.
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Magnitude of dilation
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A positive number 'r', called the magnitude of dilation, gives the relative size of the image compared with the original. This 'r' is the ratio of the corresponding lengths of the two figures.
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Corresponding altitudes
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If two triangles are similar, then altitudes drawn from the corresponding vertices are called corresponding altitudes.
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If two triangles have a correspondence between their vertices such that their corresponding sides are proportional and their corresponding angles are equal, then...
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the triangles are similar.
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