Lessons

1. Basics
 2. Deductive Reasoning
3 - Parallel lines
4 - Congruent Triangles
5 - Quadrilaterals
6 - Inequalities
7 - Similar Polygon
8 - Rt. Triangles
9 - Circles
10 - Constructions
11 - Areas of 2D objects
12 - Areas and Volumes
13 - Coordinates

 

Inequalities For One Triangle

 

Objective:

            • Learning about the inequality theorems for one triangle

 

Lesson 6-2 Inequalities for one Triangle:

Theorem 6-2

If one side of a triangle is longer than a second side, then the angle opposite the first side is larger than the angle opposite the second side.

Angle B is larger than angle C because side AB is shorter than side AC

 

Theorem 6-3

If one angle of a triangle is larger than a second angle, then the side opposite the first angle is longer than the side opposite the second angle

Corollary 1

The perpendicular segment from a point to a line is the shortest segment from the point to the line

The shortest distant from point A to line l is a perpendicular segment.

Corollary 2

The perpendicular segment from a point to a plane is the shortest segment from the point to the plane

 

Theorem 6-4

 The sum of the lengths of any two sides of a triangle is greater than the length of the third side

AB+ BC > AC

AC+ AB > BC

BC+ AC > AB

 

 

Quickie Math Copyright (c) 2000 Team C006354