Plane Geometry Chapter 4, Section 2-10: Polygons and Proving Lines Proportional

Plane Geometry Chapter 4: Proportions and Similar Polygons
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Terms to Know:

Section 2-6: Similar Polygons

Two polygons are similar if their corresponding angles are equal and their corresponding sides are proportional.
Two equal angles in two similar polygons (one angle in each polygon) are called corresponding angles.
Two sides in the two similar polygons (one side in each polygon) which join the vertices of two pairs of corresponding angles are called corresponding sides.
In the case of similar triangles, corresponding angles will always lie opposite a pair of equal.
The ratio of two corresponding sides of two similar polygons is called the ratio of similitude of the polygons.

Section 7-10: Proving Lines Proportional

C.S.S.T.P stands for corresponding sides of similar triangles are proportional.
To prove that two angles are equally based on similar triangles, use corresponding angles of similar triangles are equal. (C.A.S.T.E.)
C.A.S.T.E is another way to express the definition of similar polygons applied to triangles.

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Plane Geometry Principles in Geometry (1) A straight line is the shortest line between two points. (2) Only one straight line can be drawn between two points. (3) Two straight lines intersect at only one point. (4) Quantities (Lines) equal to the same quantity (line) are equal to each other. (5) The whole is equal to the sum of all its parts. (6) The whole is greater than any of its parts. (7) If equals are added to equals, then the sums are equal. (8) If equals are subtracted from equals then the remainders are equal. (9) Doubles of equals are equal. (10) Halves of equals are equal. (11) If the first of three quantities is greater than the second, and the second is greater than the third, then the first is greater than the third. (12) All straight lines are equal.

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