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| Theorem 6.15 |
The Law Of Sines:
Sin A/a= Sin B/b= Sin C/c, or
a/Sin A= b/ Sin B= c/Sin C |
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silentdoom Fri, 21 Nov 2008 00:30:32 GMT |
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| Thoerem 6.14 |
In a triangle with acute angle A, the sum of sin^2 A and Cos^2 A is 1.
Sin^2 A + Cos^2 A= 1 |
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silentdoom Fri, 21 Nov 2008 00:30:32 GMT |
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| Theorem 6.13 |
In a right triangle with the acute angle A, sin A divided by cos A is tan A
Sin A/Cos A= Tan A |
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silentdoom Fri, 21 Nov 2008 00:30:32 GMT |
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| Theorem 6.12 |
If ABCD is any quadrilateral and E, F, G, H are midpoints as shown, then EFGH is a parallelogram. |
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silentdoom Fri, 21 Nov 2008 00:30:32 GMT |
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| Theorem 6.11 |
Midsegment Theorem:
A midsegment of a triangle is parallel to the third side and is half its length. |
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silentdoom Fri, 21 Nov 2008 00:30:32 GMT |
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| Theorem 6.10 |
Side Splitting Theorem:
A line parallel to one side of a triangle forms a triangle similar to the original triangle and divides the other two sides of the triangle into proportional corresponding segments. |
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silentdoom Fri, 21 Nov 2008 00:30:32 GMT |
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| Theorem 6.9 |
In a right triangle, the altitude to the hypotenuse is the mean proportional between the two segments formed by the altitude on the hypotenuse. |
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silentdoom Fri, 21 Nov 2008 00:30:32 GMT |
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| Theorem 6.8 |
SSS Similarity Theorem: Two triangles are similar if three sides of one triangle are proportional to three sides of the other triangle. |
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silentdoom Fri, 21 Nov 2008 00:30:32 GMT |
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| Corollary 6.7 |
LL Similarity: Two right angles are similar if the legs of one triangle are proportional respectively to the legs of the other triangle. |
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silentdoom Fri, 21 Nov 2008 00:30:32 GMT |
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| Theorem 6.6 |
SAS Similarity Theorem:
Two triangles are similar if two sides of one triangle are proportional, respectively, to two sides of another triangle and the angles included betweenthe sides are congruent. |
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silentdoom Fri, 21 Nov 2008 00:30:32 GMT |
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| Corollary 6.5 |
Two right triangles are similar if an acute angle of one triangle is congruent to an acute angle of the other triangle. |
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silentdoom Fri, 21 Nov 2008 00:30:32 GMT |
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| Theorem 6.4 |
AA Similarity Theorem:
Two triangles are similar if two angles of one triangle are congruent, respectively, to two angles of the other triangle. |
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silentdoom Fri, 21 Nov 2008 00:30:32 GMT |
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| Postulate 6.1 |
AAA Similarity Postulate:
Two triangle are similar if and only if three angles of one triangle are congruent, respectively, to three angles of the other triangle. |
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silentdoom Fri, 21 Nov 2008 00:30:32 GMT |
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| Geometric Mean |
geometric mean of A and C is square root of AC:
A/B=B/C -> B^2=SQUAREROOT AC |
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silentdoom Fri, 21 Nov 2008 00:30:32 GMT |
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| Theorem 6.3 |
if A/B=C/D, then B is the geometric mean (mean proportional) of A and C. |
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silentdoom Fri, 21 Nov 2008 00:30:32 GMT |
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| Theorem 6.2 |
a/b=c/d if and only if D/B=C/A (exchange the extremes)
A/B=C/D if and only if A/C=B/D (exchange the means)
A/B=C/D if and only if B/A=D/C
(invert each ratio) |
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silentdoom Fri, 21 Nov 2008 00:30:32 GMT |
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| Theorem 6.1 |
Cross-Multiplication Theorem: A/B=C/D if and only if the product of the means equals the product of the extremes; A/B=B/C if AD=BC |
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silentdoom Fri, 21 Nov 2008 00:30:32 GMT |
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