Geom 7.3­7.4 ­ Triangle Inequalities and the Triangle Inequality Theorem
Angle Measures and Side Measures
Draw a triangle, and measure the three angles.
Label the largest angle C, the smallest angle A, and the middle angle B.
Measure the three sides.
Label the longest side c, the shortest side a, and the middle side b.
What do you notice?
Compare your results with your neighbors.
Theorem 7­6 and 7­7: Triangle Sides and Angles Inequality Theorem
In any triangle, the longest side(s) are opposite the largest angle(s), and the shortest side(s) are opposite the smallest angle(s). D
List the sides in order from least to greatest measure.
F
W
B
12
List the angles in order from least to greatest measure.
8
O
6
S
Geom 7.3­7.4 ­ Triangle Inequalities and the Triangle Inequality Theorem
Triangle Inequality Theorem (or, the Goat Theorem)
Triangle Inequality Theorem (or, the Goat Theorem)
In any triangle, the sum of two sides must be greater than the third side. c
a
b
Three inequalities:
_____ + _____ > _____
_____ + _____ > _____
_____ + _____ > _____
Geom 7.3­7.4 ­ Triangle Inequalities and the Triangle Inequality Theorem
Applying the Triangle Inequality Theorem
Which of the following can be measures of the sides of a triangle?
3, 5, 7
4, 7, 11
5, 5, 12
4, 7, 9
Applying the Triangle Inequality Theorem
If two sides of a triangle have the following measures, find the range of measures for the third possible side.
5, 8
2, 6