Transcript Geometry 5-5 and 5-6

Warm-Up
• Find the length of AC
C
A
B
Geometry 5-5 and 5-6
Relationships and Inequalities in
Triangles
Angle-Side Size Relationship
• Within a single triangle, the largest side will be
opposite the largest angle and the smallest
side will be opposite the smallest angle.
C
A
mB > mA
therefore
AC > BC
B
Examples
• List the sides from shortest to longest.
C
A
63
°
62
55
°
°
B
• List the angles from largest to smallest.
E
14
12
D
F
20
Angle-Size with Two Triangles
• You can use the Angle-Size theorem on two
triangles if the triangles have two congruent
sides.
F
C
mD > mA
therefore
EF > BC
A
B
D
E
Examples
Compare mBAC and mDAC.
Compare BC and AB.
Constructing Triangles
The sum of the two shortest sides must be
greater than the third side.
Example
• Tell whether the following pairs of side lengths
could construct a triangle.
7, 10, 19
6.2, 7, 9
8, 13, 21