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5.3 Notes : Inequalities in One Triangle
Vocabulary
Definition of
Inequality
Exterior Angle
Inequality
Example 1:
Use the diagram to the right.
a) Use the Exterior Angle Inequality Theorem to
list all angles whose measures are less than
measure of angle 14.
Example 1:
b) Use the Exterior Angle Inequality Theorem to
list all angles whose measures are greater than
measure angle 5.
Vocabulary:
Longest Side Vs. Longest
Angle
Smallest Side Vs.
Shortest Side
Angle-Side
Relationships in
Triangles (5.9)
Angle- Side
Relationships in
Triangles (5.10)
Example 2:
Example 2: List the angles of ΔABC in order from
smallest to largest.
Example 3:
Example 3: List the sides of ΔABC in order from
shortest to longest.
Example 4:
Example 4: 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 5:
List the angles of each triangle in order from
smallest to largest.
Example 6:
List the angles of each triangle in order from
smallest to largest.
Example 7:
• List the angles of each triangle in order from
smallest to largest.
∆XYZ, where XY = 25, YZ = 11, and XZ = 15
Example 8:
List the sides of each triangle in order from
shortest to longest.
Example 9:
List the sides of each triangle in order from
shortest to longest.
5.1-5.3 Vocabulary Skills Check
Match each word to the sentence in which it best fills in the blank. Write your answer on the line to
the left.
_____1) The point of intersection of the angle bisectors in a triangle is called the_?_.
_____2) The _?_ divides the medians in a triangle into the parts.
_____3) The centroid is the intersection of the_?_in a triangle.
_____4) The circumcenter is equidistant from the _?_in a triangle.
_____5) The incenter is equidistant from the_?_in a triangle
_____6) The point of intersection of the perpendicular bisectors in a triangle is called the_?_.
_____7) The altitudes in a triangle intersect at a point called the _?_.
Summary!
a) List the sides from biggest to smallest. Write
your answer as an inequality.
Summary!
b) List the angles from largest to smallest. Write
your answer as an inequality.
A
25
12
W
15
P