This document discusses properties of triangles related to side lengths and angles. It states that 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. It also states that if one angle is larger than a second angle, then the side opposite the first angle is longer than the side opposite the second angle. The document then asks the reader to identify the longest and shortest sides of a triangle based on these properties.

1. 6-4 Inequalities in One Triangle

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.
Answers: smallest is
Z; largest is
Y

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.
Name the longest side and the shortest side.

4. 
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.

5. 


The sum of the lengths of any two sides of a
triangle is greater than the length of the third
side.
Is it possible for a triangle to have sides with
lengths 9, 6, and 2?
Two sides of a triangle have lengths 8 and
12. The length of the third side can be any
number between _____ and _____.
Answers: no; 4 and 20