Inverses, Contrapositives, and Indirect Reasoning

1
Inverses, Contrapositives, and Indirect Reasoning
GEOMETRY LESSON 5-4
I and III
5-4
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Inequalities in Triangles
GEOMETRY LESSON 5-5
(For help, go to Lesson 1-6 and 5-4.)
INVESTIGATION In your group graph each set of
points, one per graph. Connect the points to form
a triangle. Measure each angle of the triangle
and write the measurement in the angle. Measure
each side of the triangle in cm and write the
measurement on that side.
1. A(5, 0), B(0, 8), C(0, 0) 2. P(2, 4), Q(5,
1), R(0, 0) 3. G(3, 0), H(4, 3), J(8, 0) 4.
X(4, 3), Y(1, 1), Z(1, 4) What do you
notice?
5-5
3

• 5.5 Inequalities in Triangles.
• Objective
• learn and use inequalities involving angles and
  sides of triangles.

4
Theorems and Corollaries
5
Simply put

• The shortest side is opposite the smallest
  angle, the longest side is opposite the largest
  angle.

6
Inequalities in Triangles
GEOMETRY LESSON 5-5
5-5
7
Inequalities in Triangles
GEOMETRY LESSON 5-5
5-5
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Inequalities in Triangles
GEOMETRY LESSON 5-5
5-5
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Inequalities in Triangles
GEOMETRY LESSON 5-5
According to the Triangle Inequality Theorem, the
sum of the lengths of any two sides of a
triangle is greater than the length of the third
side.
a. 2 2 gt 4 No. The sum of 2 and 2 is not
greater than 4, contradicting Theorem 5-12.
b. 8 15 gt 12 8 12 gt 15 15 12 gt 8
Yes. The sum of any two lengths is greater than
the third length.
5-5
10
Inequalities in Triangles
GEOMETRY LESSON 5-5
In FGH, FG 9 m and GH 17 m. Describe the
possible lengths of FH.
The Triangle Inequality Theorem states the sum of
the lengths of any two sides of a triangle is
greater than the length of the third side.
Solve three inequalities.
26 gt FH This can be written FH lt 26.
FH gt 8 This can be written 8 lt FH.
FH gt 8
5-5