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# Triangle Inequalities (PowerPoint)

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```									    Inequalities in One
Triangle
Objectives:
 Use triangle measurements to decide which side
is longest or which angle is largest
 Apply the Triangle Inequality
Which side is larger, AC or BC?
B
5       BC > AC

A             C
3
Which angle is larger B or A?
B               A > B
5

A            C
3
Theorem: Side Angle
one side of a triangle is
 If
longer than another side,
then the angle opposite the
longer side is larger than
the angle opposite the
shorter side.
Which angle is larger, D or F?
D          F > D
24

40
E              F
Which side is larger, DE or EF?
D                 DE > EF
24

40
E             F
Ex. 1 Write the angles in order from least to
greatest.

A                     C, A, B
52
12
B                               C
43
Theorem: Angle Side
one angle of a triangle is
 If
larger than another angle,
then the side opposite the
larger angle is longer than
the side opposite the
smaller angle.
Ex. 2 Write sides in order from greatest to
least.
Y
XZ, XY, YZ
128º
22º               30º      Z
X
81

54         45
Theorem: Exterior Angle Inequality
The measure of an
exterior angle of a   1
triangle is greater
than the measure
of either of the
interior angles.
2            3
Which angle is larger 2 or 3? 2  3
Which angle is larger 1 or 3? 1  3
Constructing a
Triangle
Not every group of 3
segments can be used to
form a triangle.
How can you tell if it is possible
for three sides to form a triangle?

The 2 smaller sides must add up to be
MORE THAN the largest side.
Triangle Inequality Theorem
The sum of the
lengths of the two
C     smaller sides must be
greater than the
B
length of the 3rd side.
A
Determine if the three numbers can be measures of
the sides of a triangle. If no, explain.
a. 13, 28, 19                    ?
13  19  28         Yes

b. 8, 4 2 , 4 2                   ?
4 2  4 2  8 Yes
c. 28, 96, 124
?
28  96 124 NO
Finding Possible Side Lengths
If two sides of a triangle have the
following measures, find the range of
possible measures of the third side.
a. 10, 7             b. 18 , 11

3 < x < 17           7 < x < 29
Practice

p. 287 #1 – 23 odd
(12 problems)

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