1. Lesson 5-3 Inequalities in one Triangle

2. Vocabulary Theorem 5.8: Exterior Angle Inequality
The measure of an exterior angle of a triangle is greater than the measure of either of its corresponding remote interior angles.

3. Example 1 A. B. C. D.

4. Example 1 A. B. C. D.

5. Vocabulary Theorem 5.9: Angle-Side Relationship #1
If one side of a triangle is longer than another side, then the angle opposite the longer side has a greater measure than the side opposite the shorter side.

6. Vocabulary Theorem 5.10: Angle-Side Relationship #2
If one angle of a triangle has greater measure than another angle, then the side opposite the greater angle is longer than the side opposite the lesser angle.

7. Example 2 List the angles of ΔABC in order from smallest to largest.
Order Triangle Angle Measures
List the angles of ΔABC in order from smallest to largest.
Answer: C, A, B

8. Example 2 List the angles of ΔTVX in order from smallest to largest.
A. X, T, V
B. X, V, T
C. V, T, X
D. T, V, X

9. Example 3 List the sides of ΔABC in order from shortest to longest.
Order Triangle Side Lengths
List the sides of ΔABC in order from shortest to longest.
The angles from smallest to largest are B, C, and A. The sides opposite these angles are AC, AB, and BC, respectively. So, the sides from shortest to longest are AC, AB, BC.
Answer: AC, AB, BC

10. Example 3 List the sides of ΔRST in order from shortest to longest.
A. RS, RT, ST
B. RT, RS, ST
C. ST, RS, RT
D. RS, ST, RT

11. Example 4
Angle-Side Relationships
HAIR ACCESSORIES Ebony is following directions for folding a handkerchief to make a bandana for her hair. After she folds the handkerchief in half, the directions tell her to tie the two smaller angles of the triangle under her hair. If she folds the handkerchief with the dimensions shown, which two ends should she tie?
Answer: So, Ebony should tie the ends marked Y and Z.

12. Example 4
KITE ASSEMBLY Tanya is following directions for making a kite. She has two congruent triangular pieces of fabric that need to be sewn together along their longest side. The directions say to begin sewing the two pieces of fabric together at their smallest angles. At which two angles should she begin sewing?
A. A and D
B. B and F
C. C and E
D. A and B