Study Geometry Flash Cards

 
Pile Management Card
Geometry

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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
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
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
Theorem 6.12
If ABCD is any quadrilateral and E, F, G, H are midpoints as shown, then EFGH is a parallelogram.
Theorem 6.11
Midsegment Theorem:
A midsegment of a triangle is parallel to the third side and is half its length.
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.
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.
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.
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.
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.
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.
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.
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.
Geometric Mean
geometric mean of A and C is square root of AC:

A/B=B/C -> B^2=SQUAREROOT AC
Theorem 6.3
if A/B=C/D, then B is the geometric mean (mean proportional) of A and C.
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)
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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