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17 Cards in this Set
- Front
- Back
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ratio
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the ratio of x to y (y can't=0)is x/y and is sometimes written x:y. It is expressed in simplest form.
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proportion
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an equation stating that two ratios are =.
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term of a proportion
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a proportion in the form a/b=c/d; a is the first term, b is the second and so on.
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extended proportion
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an equation showing that three or more ratios are =
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extremes of a proportion
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the first and last terms
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means of a proportion
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the middle terms
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means-extremes property of proportions
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the product of the means = the product of the extremes
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Properties of Proportions
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1. a/b=c/d is equivalent to
a) ad=bc b) a/c=b/d c) b/a= d/c d)(a+b)/b= (c+d)/d 2. if a/b=c/d=e/f=..., then a+c+e+.../b+d+f+...=a/b=... |
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two polygons are similar if...
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their vertices can be paired so that:
1) <-. angles are congruent 2)<-> sides are in proportion |
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scale factor
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if two polygons are similar, then the ratio of the lengths of two <->sides
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AA similarity postulate
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If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar
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SAS Similarity theorem
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If an angle of one trianle is congruent to an angle of another triangle and the sides including those angles are in proportion, then the triangles are similar
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SSS Similarity theorem
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If the sides of two triangles are in proportion, then the triangles are similar
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divided proportionally
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If points L and M lie on line AB and line CD, respectively, and AL/LB=CM/MD, then line AB and line CD are divided proportionally
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Triangle Proportionality Theorem
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If a line parallel to one side of a triangle intersects the other two sides, then it divides those side proportionally
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If three parallel lines intersect two transversals,....
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then they divide the transversals proportionally
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Triangle Angle Bisector Theorem
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If a ray bisects an angle of a triangle, then it divides the opposite side into segments proportional to the other two sides
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