Chapter 8: Similar Polygons

To the left, you see a glorious motion picture of a HYPERCUBE. This demonstrates the fourth dimension and is not at all related to this chapter.
When you manage to tear your eyes from it, we will continue with our review. You could also continue looking at it and flunk the final. Your choice.
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In the eighth chapter of the textbook Geometry for Enjoyment and Challenge, the author(s) demonstrated the use of similar polygons in geometry.
RATIO:
a quotient of two numbers a:b or a/b

PROPORTION:
equation stating that ratios are equal

GEOMETRIC MEAN:
a proportion in which the means are equivalent a / x=x / d
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ARITHMETIC MEAN: the average of two numbers x=(a+d) / 2 I don't think we used this outside of the first section.
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SIMILAR FIGURES: same shape but not necessarily the same size.
These are turtles. I've always wanted a turtle. I got an cat instead. He's fat.
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In SIMILAR POLYGONS:The corresponding sides are proportional

The ratio of the perimeters are equal

Corresponding angles are congruent

△ABC∼△XYZ

c/a=z/x c/b=z/y a/b=x/y etc.

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You can proove that triangles are similar if:

2 angles are congruent AA∼ or AA∼

3 sides' ratios are equal SSS∼

2 sides' ratios and the included angles are congruent SAS∼

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CSSTP: Corresponding Sides of Similar Triangles are Proportional

CASTC: Corresponding Angles of Similar Triangles are Congruent

I don't know if you can use that abbreviation but there you go.

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SIDE SPLITTER THEOREM

A line divides two sides of a triangle prop

ortionally if it is parallel to the the third.

If parallel lines are intersected by two transversals, the parallel lines divide them proportionally.

ANGLE BISECTOR THEOREM

If a ray bisects a

 triangle's angle; it divides the opposite side into segments proportional to the adjacent sides.

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AND that is about it... have fun studying and GOOD LUCK

~~~~~~OLIVIA~~~~~~