Transcript PowerPoint

6.4 Triangle Inequalities
Angle and Side Inequalities
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Sketch a good size triangle in your notebook
(about a third of the page).
Using a ruler find the approximate length of each
side (in inches or centimeters).
How is the largest side related to the largest
angle?
How is the smallest angle related to the smallest
side?
Name the angles in ascending
order.
B
18
21
A
19
C
mC
mB
mA
Name the longest side. AB
Name the shortest side. BC
B
AB
58o
A
43o
79o C
TRIANGLE INEQUALITY THEOREM
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The sum of the lengths of any two
sides of a triangle is greater than the
length of the third side.
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Is it possible for a triangle to have the following
lengths?
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9 >>863
11
YES
3, 6, 8 63 + 86 = 14
10, 10, 0.5 0.5
10==20
10.5
> 10 YES
10 ++10
> 0.5
Get on your “Thinking Caps”
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Can you think of three lengths
that cannot make a triangle?
More Triangle Inequality Practice
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The lengths of two sides of a
triangle are 3 and 5. The length of
the third side must be greater than
5 2- 3
and less than 5 +8 3 .
Put the following angles in ascending order.
1, 2, X , Y , XZY
There are 3 triangles involved!
NOTE: We DO NOT KNOW that ZW  XY !!
Z
1
15
13
12
2
X
5
W
9
Y
Section 6.4 #17
NOTE: We DO NOT KNOW that ZW  XY !!
Label XWZ and XZW
There are 3 triangles involved!
2>Y>1
3>X>4
ZZ
44 11
15
15
13
12
12
33 22
X
5
YY
99
W
W
Using WXZ
Using
we get:
XYZUsing
we get:WYZ we get:
Z
2>X
Z
Z
1
4
15
X > XZY > Y
13
13
12
Now we can make our list:
3 2
X
X5
W
15
12
2
W
14
9
And... 2 > X
m2 > mX > mXZY > mY > m1
(Ext. Angle)
YY
PRACTICE MAKES PERFECT!
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Page 221
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#1 – 16
Extra Credit Opportunity (SAT style!)
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What is the smallest integer, x, for which
x, x + 5, and 2x – 15 can be the lengths of the
sides of a triangle?
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Hint: Use the Triangle Inequality Theorem