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GHLesson 53_notes.notebook November 02, 2015
53 Inequalities in One Triangle
Students will be able to . . .
• recognize and apply properties of inequalities to the measures of the angles of a triangle.
• recognize and apply properties of inequalities to the relationships between the angles and sides of a triangle.
What do we already know about 1?
How does the m 1 compare to the m 2?
How does the m 1 compare to the m 3?
1
2
3
GHLesson 53_notes.notebook November 02, 2015
Exterior Angle Inequality
The measure of the exterior angle of a triangle is greater than the measure of either of the remote interior angles.
Since the measure of an angle and the length of a segment are represented by real numbers, the definition of inequality and the properties of inequalities can be applied.
1
2
3
m 1 > m 2
m 1 > m 3
GHLesson 53_notes.notebook November 02, 2015
GHLesson 53_notes.notebook November 02, 2015
GHLesson 53_notes.notebook November 02, 2015
A
B
C
In ΔABC, which angle appears to be the largest?
Which side appears to be the longest?
Which angle appears to the smallest?
Which side appears to the the shortest?
How would you describe the location of the longest side in comparison to the largest angle?
shortest side to the smallest angle?
GHLesson 53_notes.notebook November 02, 2015
Write the complete inequality. Use the proper notation!
GHLesson 53_notes.notebook November 02, 2015
Write the complete inequality. Use the proper notation!
GHLesson 53_notes.notebook November 02, 2015
Additional Practice
List the sides and angles in order from smallest to largest.
Which segment in the figure is the longest?
