5-3

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Transcript 5-3 

5-3 Inequalities in One Triangle
You found the relationship between the angle
measures of a triangle.
• Recognize and apply properties of
inequalities to the measures of the angles of
a triangle.
• Recognize and apply properties of
inequalities to the relationships between the
angles and sides of a triangle.
Page 344
The definition of inequality and the
properties of inequalities can be applied to
the measures of angles and segments,
since these are real numbers.
2
1
3
By the Exterior Angle Inequality Theorem, m14 > m4
and m14 > m11. In addition, m14 > m2 and
m14 > m4 + m3, so m14 > m4 and m14 > m3.
Since 11 and 9 are vertical angles, they have
equal measure, so m14 > m9. m9 > m6 and
m9 > m7, so m14 > m6 and m14 > m7.
A.
B.
C.
D.
The Littlest Angle
1.
2.
3.
4.
A
Draw a scalene triangle.
Measure the three sides.
Measure the three angles.
What relationship do you see
between the sides and the
angles?
C
B
Name the largest and smallest
angles
A
9
C
B
12
Name the largest and smallest
angles
D
5.6
110°
E
5.5
F
List the angles of ΔABC in order from
smallest to largest.
The sides from the shortest to longest are AB,
BC, and AC. The angles opposite these sides are
C, A, and B, respectively. So, according to
the Angle-Side Relationship, the angles from
smallest to largest are C, A, B.
Answer: C, A, B
Name the longest and shortest
segments
A
30°
130°
B
20°
C
Name the longest and shortest
segments
V
49°
W
X
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
Theorems
If two sides of a triangle have unequal
lengths, then the measure of the angle
opposite the longer side is greater than
the measure of the angle opposite the
shorter side.
If two angles of a triangle have unequal
measures, then the side opposite the
large angle is longer than the side
opposite the smaller angle
5-3 Assignment
• Page 348, 8-12, 1419, 22-28 even