Download Lesson 5.3

Lesson 5-3 Inequalities in one
Triangle
Theorem 5.8:
Vocabulary
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.
Example 1
A.
B.
C.
D.
Example 1
A.
B.
C.
D.
Theorem 5.9:
Vocabulary
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.
Theorem 5.10:
Vocabulary
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.
Example 2
Order Triangle Angle Measures
List the angles of ΔABC in order from smallest to largest.
Answer:
C, A, B
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
Example 3
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
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
Example
4Relationships
Angle-Side
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.
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