Aim: What is Triangle Inequality?
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Course: Applied Geometry Aim: What is Triangle Inequality Theorem Aim: What is Triangle Inequality? Do Now: Sketch 9
description
Aim: What is Triangle Inequality?. Do Now: Sketch 9. Triangle Inequality Theorem. The sum of the lengths of any two sides of a triangle is greater than the length of the third side. Y. XY + YZ > XZ. YZ + XZ > XY. XZ + XY > YZ. X. Z. Triangle Inequality Theorem. - PowerPoint PPT Presentation
Transcript of Aim: What is Triangle Inequality?
Course: Applied GeometryAim: What is Triangle Inequality Theorem
Aim: What is Triangle Inequality?
Do Now: Sketch 9
Course: Applied GeometryAim: What is Triangle Inequality Theorem
The sum of the lengths of any two sides of a triangle is greater than the
length of the third side.
Y
ZX
XY + YZ > XZ
YZ + XZ > XY
XZ + XY > YZ
Course: Applied GeometryAim: What is Triangle Inequality Theorem
The length of the third side must be somewhere in between the
SUM and the DIFFERENCE of the lengths of the first two sides.
Y
ZX
XY – YZ < XZ < YZ + XY
Course: Applied GeometryAim: What is Triangle Inequality Theorem
TRIANGLE FORMED?
Lengths of SegmentsNo. 1 No. 2 No. 3
TriangleFormed?
1 2 33 4 55 5 41.5 2.5 3.55 1/2 5 3/4 116 10 1330 60 90
NO
YES
YES
YES
YES
NO
YES
Course: Applied GeometryAim: What is Triangle Inequality Theorem
Is it possible to form a triangle with side lengths 4 cm., 6 cm., and 10 cm.? Explain
No, 6 + 4 is not > 10, even though 6 - 4 = 2 < 10
Is it possible to form a triangle with side lengths 10 cm., 8 cm., and 3.5 cm.? Explain
yes, 10 + 8 > 3.5 and 10 - 8 = 2 < 3.5
Model Problems
Course: Applied GeometryAim: What is Triangle Inequality Theorem
The lengths of two sides of a triangle are given. Write an inequality to represent the range of values for z, the length of the third side.
Model Problems
8 ft, 12 ft.
4 < z < 20
6 cm, 6 cm
0 < z < 12 12
8
66
Course: Applied GeometryAim: What is Triangle Inequality Theorem
5 7
CB
A
9
A, B, OR C? Which is the largest angle
of ABC?
Which is the smallest?
A
C
If one side of a triangle is greater in measure than a second side, then the angle opposite the first side is greater in measure than the angle opposite the second side.
If BC > AC, then mA > mB.
If mA > mB, then BC > AC.
Also true
Model Problems
Course: Applied GeometryAim: What is Triangle Inequality Theorem
In a triangle, the angle with the smallest measure is opposite the shortest side of the triangle. The angle with the greatest measure is opposite the longest side of the triangle.
Y
ZX
m___ < m___ < m___
Fill in the blanks
Segments:
Angles:
___ < ___ < ___
Conjecture:
Z X Y
xz
y
z x y
Who’s Bigger?
Course: Applied GeometryAim: What is Triangle Inequality Theorem
Who’s Bigger?
List the angles of each triangle in order from smallest to largest.
4
86
B
CA
5.8
5.2
2.3T
S
R
B < C < A S < T < R
Course: Applied GeometryAim: What is Triangle Inequality Theorem
Model Problems
List the sides of each triangle in order from shortest to longest.
450
750H
K
J
HJ < JK < HK
60o
BC < AC < AB
6001350
A
C
B45o
75o
Course: Applied GeometryAim: What is Triangle Inequality Theorem
A triangle has sides measuring 3, 5, and 7. Is it a right triangle? If not what type?
The Pythagorean Theorem, a2
+ b2 = c2 will show us if it’s a right triangle. 7 would be the measure of the hypotenuse.
32 + 52 = 72 9 + 25 = 49 Not a right ?
a2 + b2 < c2
a2 + b2 > c2
Obtuse
Acute
a = 3, b = 5, c = 7
32 + 52 = 72 34 < 49 Obtuse or acute?
What Type of Triangle?
Course: Applied GeometryAim: What is Triangle Inequality Theorem
The numbers represent the length of the sides of a triangle. Classify each as acute, obtuse, or right.
What Type of Triangle?
13, 84, 85
a2 + b2 < c2
a2 + b2 > c2
Obtuse
Acute
132 + 842 = 852
169 + 7056 = 7225
7225 = 7225
rt. triangle
6, 11, 14 62 + 112 = 142
36 + 121 = 196157 < 196
obtuse triangle
11 + 7 = 1618 > 16
acute triangle
11, 7,4 2 211 7 16
