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Geometry
January 9, 2017
5.6/5.7 Triangle Inequalities
DO NOW
Δ𝐴𝐵𝐶 is a triangle. For each pair of angles, what
is 𝑚∠𝐶?
1. 𝑚∠𝐴 = 90°; 𝑚∠𝐵 = 40°
2. 𝑚∠𝐴 = 75°; 𝑚∠𝐵 = 30°
3. 𝑚∠𝐴 = 28°; 𝑚∠𝐵 = 111°
4. 𝑚∠𝐴 = 31°; 𝑚∠𝐵 = 49°
Agenda
• Announcements (2nd hour only)
• Do Now
• Review: Inequalities in a Triangle
• Practice
• Notes: Inequalities in two triangles
I can identify and apply
triangle midsegments,
medians, and altitudes.
Triangle Inequalities
1. An exterior angle is always larger than
either remote interior angle.
Triangle Inequalities
2. Larger angles are always opposite larger
sides (and vice versa).
Triangle Inequalities
3. The lengths of the two shorter sides of a
triangle are more than the length of the
longest side.
Practice
Hinge Theorem (aka SAS/SSS Inequality)
∠𝐴 > ∠𝑋 ⇔ 𝐵𝐶 > 𝑌𝑍
Hinge Theorem (aka SAS Inequality)
• Write an inequality statement.
Hinge Theorem (aka SAS Inequality)
• Write an inequality statement.
Hinge Theorem (aka SSS Inequality)
• What are the possible values of x:
• What is the lowest it could be?
• What is the highest it could be?
Hinge Theorem (aka SSS Inequality)
• What are the possible values of x:
• What is the lowest it could be?
• What is the highest it could be?
Hinge Theorem (aka SSS Inequality)
• What are the possible values of x:
• What is the lowest it could be?
• What is the highest it could be?
Practice