PREPARING Become a MATIZEN What is Math Planet ? A Crash Course on      Algebra A Crash Course on      Geometry   EXPLORING Advanced Math Topic Customized Lessons SAT & ACT Reviews   INTERACTING Math Games Discussion Forum Math Live! Chat   COLLECTING Math Search MATIZEN Qualifi-      -cation Test Acknowledgements The Creatures Behind      the Math Planet     ©1998 ThinkQuest team 16284 All rights reserved

# Part 4

 Theorem 5.9 Any point on the perpendicular bisector of a segment is equidistant from the endpoints of the segment. Theorem 5.10 Exterior Angle Inequality Theorem: The measure of an exterior angle of a triangle is greater than the measure of either of its remote interior angles. Theorem 5.11 If one side of a triangle is longer than another side, then the measure of the angle opposite the longer side is greater than the measure of the angle opposite the shorter side. Theorem 5.12 If one angle of a triangle has a greater measure than a second angle, then the side opposite the greater angle is longer than the side opposite the smaller angle. Theorem 5.13 In a scalene triangle, the longest side is opposite the largest angle and the largest angle is opposite the longest side. Theorem 5.14 The perpendicular segment from a point to a line is the shortest segment from the point to the line. Corollary The longest side of a right triangle is the hypotenuse. Theorem 5.15 Triangle Inequality Theorem: The sum of the lengths of any two sides of a triangle is greater than the length of the third side. Theorem 5.16 SAS Inequality Theorem: If two sides of one triangle are congru- ent, respectively, to two sides of a second triangle, and the included angle of the first triangle has a greater measure than the included angle of the second triangle, then the third side of the first triangle is longer than the third side of the second triangle. Theorem 5.17 SSS Inequality Theorem: If two sides of one triangle are congruent, respectively, to two sides of a second triangle, and the length of the third side of the first triangle is greater than the length of the third side of the second triangle, then the angle opposite the third side of the first triangle has a greater measure than the angle opposite the third side of the second triangle. Theorem 6.1 The sum of the measures of the interior angles of a convex polygon with n sides is (n - 2)180. Corollary 1 The sum of the measures of the interior angles of a convex quadrilateral is 360. Corollary 2 The measure of an angle of a regular polygon with n sides is(n - 2)180/n. Theorem 6.2 The sum of the measures of the exterior angles, one at each vertex, of any convex polygon is 360. Corollary The measure of an exterior angle of a regular polygon with n sides is 360/n.

.

Note: The concepts in this collection may not be entirely accurate.
They are for reference only.