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Definition
The quotient when the first number is divided by the second
The ratio of 8 to 12 is 8/12 or 2/3
Pg. 241 |
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Definition
An equation stating that two ratios are equal
a/b = c/d and a:b = c:d
Pg. 242 |
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Definition
The first and last term of a proportion are called the extremes. The middle terms are the means.
a:b = c:d 6:9 = 2:3 6/9 = 2/3
a, c, 6, & 3 are the Extremes
b,c,9, & 2 are the means
Pg. 245 |
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| Properties of Proportions |
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Definition
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 = ...
Pg. 245 |
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Definition
Two polygons are similar if their vertices can be paired so that:
1. Corresonding <s are ≅
2. Corresponding sides are in porportion (Their lengths have the same ratio)
Pg. 249 |
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Definition
The ratio of the lengths of two corresponding sides of two similar polygons.
Pg. 249 |
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Postulate 15
AA Similarity |
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Definition
If two <s of one Δ are ≅ to two <s of another Δ, then the Δ's are similar.
Pg. 255 |
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Theorem 7-1
SAS Similarity |
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Definition
If an < of one Δ is ≅ to an < of another Δ and the sides including those <s are in proportion, then the Δ's are similar.
Pg. 263 |
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Theorem 7-2
SSS Similarity |
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Definition
If the sides of two Δ's are in proportion, then the Δ's are similar.
Pg. 263 |
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Theorem 7-3
Δ Proportionality |
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Definition
If a line II to one side of a Δ intersects the other two sides, then it divides those sides proportionally.
Pg. 269 |
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Corollary 1
of Theorem 7-3 |
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Definition
If three II lines interest two transversals, then they divide the transversals, proportionally.
Pg. 270 |
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Definition
If a ray bisects an < of a Δ, then it divides the opposite side into segments proportional to the other two sides.
Pg. 270 |
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