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Chapter 7 Geometry Flashcards
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Terms in this set (17)
A Ratio
A ratio is the quotient of two numbers, usually written as a/b or a:b (b cannot = 0) A ratio is usually expressed in simplest form.
A Proportion
An equation that states that two ratios are equal.
a/b = c/d (the means or the inside numbers of a:b = c:d which are b and c are equal to the extremes which are a and d, due the cross multiplication)
An Extended Proportion
An equation relating three or more ratios.
How Many Terms are in a Proportion?
4. a/b = c/d, a being the 1st term, b being the second, c being the third d being the fourth term.
Means and Extremes Proportion Property
The product of the means is equal to the extremes.
Interchanging Means Proportion Property
If you interchange the means, you get an equivalent proportion.
Reciprocal Ratio Proportion Property
If you take the reciprocals of the ratios, the result is an equivalent proportion.
Add One To Both Sides Proportion Property
If you add one to both sides, you still have an equivalent proportion.
Extended Proportion Property
In an extended proportion, the ratio of the sum of all the numerators to the sum of all the denominators is equivalent to each of the original ratios.
Similar Polygons
Two polygons are similar if their vertices can be paired so that corresponding angles are congruent and corresponding sides are in proportion.
Scale Factor
If two polygons are similar, then corresponding sides are in proportion. The ratio of the lengths of any two corresponding sides is called the scale factor of the similarity. Labeled as A' (A prime)
AA Similarity Postulate
If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
SAS Similarity Postulate
If an angle of one triangle is congruent to an angle of
another triangle and the sides including those angles are in proportion, then the triangles are similar.
SSS Similarity Postulate
If the sides of two triangle are proportional to the three sides of another triangle, the the triangles are similar.
Triangle Proportionality Theorem
If a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides proportionally.
Triangle Angle-Bisector Theorem
If a ray bisects an angle of a triangle, then it divides the opposite side into segments proportional to the other two sides.
Corollary Triangle Proportionality Theorem
If three parallel lines intersect two transversals, then they divide the transversals proportionally.
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