1. INEQUALITIES Sides/Angles of Triangles
Geometry 5.2
Objectives:
Learn the Exterior Angle INEQUALITY Theorem
To Recognize the LONGEST Side from the
Largest Angle
To Recognize the LARGEST Angle from the
Longest Side

2. A REMINDER about INEQUALITIES
If a > b if there exists a positive number c such that
b + c = a
If a < b if there exists a positive number c such that
a + c = b

3. EXTERIOR ANGLE INEQUALITY Theorem
The measure of an EXTERIOR Angle of a Triangle
is GREATER Than
the measure of EITHER of its REMOTE INTERIOR Angles.

4. EXTERIOR ANGLE INEQUALITY Theorem
The measure of an EXTERIOR Angle of a Triangle
is GREATER Than
the measure of EITHER of its REMOTE INTERIOR Angles. C 3 2 1 A D B

5. INEQUALITY Algebra
Assume: a > b
1. If b > c, then a > c (Transitive)

6. INEQUALITY Algebra
Assume: a > b
1. If b > c, then a > c (Transitive)
2. If c = d, then a + c > b + d (Algebra)

7. INEQUALITY Algebra
Assume: a > b
1. If b > c, then a > c (Transitive)
2. If c = d, then a + c > b + d (Algebra)
If c > d, then a + c > b + d (Algebra)

8. INEQUALITY Algebra
Assume: a > b
1. If b > c, then a > c (Transitive)
2. If c = d, then a + c > b + d (Algebra)
If c > d, then a + c > b + d (Algebra)
4. If b = c, then a > c (Substitution)

9. LONGEST SIDE - BIGGEST ANGLE TheoremIF
ONE SIDE of a Triangle is LONGER than another side,
THEN
the Angle OPPOSITE the Longer Side is GREATER
than the Angle OPPOSITE the Shorter Side.

12. LONGEST SIDE - BIGGEST ANGLE Th.R Q P
Given:
Prove:
WITHOUT using the BIGGEST Angle LONGEST Side Theorem

13. TRICHOTOMY Property
For any TWO Real Numbers a and b,
Only ONE of THREE Possible Relationships Exists:
a < b or
a = b
a > b

14. BIGGEST ANGLE - LONGEST SIDE Th.IF
ONE Angle of a Triangle is GREATER THAN a
SECOND Angle,
THEN
The Side OPPOSITE the GREATER Angle is LONGER
than the Side OPPOSITE the Smaller Angle.

15. BIGGEST ANGLE - LONGEST SIDE Th.R Q P
Given:
Prove: RQ > RP

20. HUGE D 58 56 A 63 59 70 54 B C
Name the LONGEST Segment.

21. S 65 60 R 55 70 P 60 50 Q
The LONGEST Segment is?

22. R 1 Q P S
Given:
Prove:

23. D C 1 3 2 B A
Given:
Prove: BD > AD

24. Geometry 5.2
You should be able to:
State the Exterior Angle INEQUALITY Theorem
Identify the LONGEST Side from the
Largest Angle
Identify the LARGEST Angle from the
LONGEST Side