Download 4.7 Triangle Inequalities - Parkway C-2

4.7 Triangle Inequalities
Theorem 4.10
• If one side of a triangle is longer than
another side, then the angle opposite the
longer side is larger than the angle opposite
the shorter side.
A
5
IF BC > AC, then m<A > m<B
B
13
C
Theorem 4.11
• If one angle of a triangle is larger than
another angle, then the side opposite the
larger angle is longer than the side opposite
the smaller angle.
D
IF m<F > m<E, then DE >DF
F
60°
40° E
B
10
4
A
C
8
Name the angles from largest to smallest.
D
58°
86°
37°
E
Name the sides from longest to shortest
F
Theorem 4.12
• The sum of the lengths of any two sides of a
triangle is greater than the length of the
third side.
CA + AB > BC
B
AB + BC > CA
BC + CA > AB
A
C
Can the side lengths form a triangle?
•
•
•
•
•
•
3, 5, 9 ?
3, 5, 8 ?
3, 5, 7 ?
5, 7, 13 ?
6, 9, 12 ?
10, 15, 25 ?