Honors Geometry
Name: ________________________
6.4 Class Notes
Date: ___________________Pd:___
Inequalities in Triangles
Warm Up:
1. Prove Directly: If x and z are multiples of y, then x+z is a multiple of y.
2.
Given: Points R, S, T and W; RS and TW are skew
Prove: RT and SW are skew
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.
R
Z
3
T
1
2
S
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.
R
T
S
Corollary 1: The perpendicular segment from a point to a line is the shortest segment from the point to the
line.
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 Triangle Inequality Theorem: The sum of the lengths of any two sides of a triangle is
greater than the length of the third side.
C
A
B
Z
Example 1) The length of two sides of a triangle are 3 and 5. The length of the third side must be…
Homework: p. 222 #1-12 all
p.223 #13-20 all