Transcript 5.3 Notes written

5.3 Inequalities in One Triangle
Then: You found the relationship between
the angle measures of a triangle.
Now:
1. Recognize and apply properties of
inequalities to the measure of the
angles of a triangle.
2. Recognize and apply properties of
inequalities to the relationship
between the angles and sides of a
triangle.
Angle Inequality:
*Properties of inequalities can be used with
measures of angles and segments.
See Key Concept p. 344.
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.
Angle Inequality
Exterior Angle Inequality Theorem:
and
m1  m  A
m1  m  B
Example 1:
Use the Exterior Angle
Inequality Theorem to
list all of the angles
that satisfy the
stated condition.
a. Measures are less than m  1
b. Measures are greater than m  1
b. Measures are less than m  7
Example 1:
d. Measures are greater than m  2
e. Measures are greater
than m 5
f. Measures are less
than m 4
Inequalities in One Triangle
B
A
E
C
ABC
F
D
DEF
Largest angle
Longest side
Smallest angle
Shortest side
How are angle and side measures related?
Angle-Side Relationships
in Triangles
Theorem 5.9: If one side of a triangle is
longer than another side, then the angle
opposite the longer side has a greater
measure than the angle opposite the shorter
side.
CB  AB, so mA  mC
Angle-Side Relationships
in Triangles
Theorem 5.10: If one angle of a triangle has
a greater measure than another angle,
then the side opposite the greater angle is
longer than the side opposite the lesser
angle.
mB  mC, so AC  AB
http://www.wyzant.com/Help/Images/inequality10.gif
Example 2:
List the angles and sides in order from
smallest to largest.
a.
b.
Example 3:
List the angles and sides in order from
smallest to largest.
Example 4:
a. 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?
Example 4:
b. List the sides of ABC in order from smallest to
largest if the angles of ABC have the indicated
measures.
mA = 5x + 2
m B = 6x -10
m C = x + 20
Example 4:
c. Order the sides from shortest to longest.
D
A
55
50
65
B
70
C
5.3 Assignment
p. 348-351
#8-11, 14-22 evens, 23, 24,
26-40 evens, 41, 44, 48, 51, 52