Problem 3 Using Theorem 5-11
Multiple Choice Which choice shows the sides of
Plan
How do you use the angle measures to order the side lengths?
List the angle measures in order from smallest to largest. Then replace the measure of each angle with the length of the side opposite.
By the Triangle Angle-Sum Theorem,
✓ Got It?
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Reasoning In the figure below,
For three segments to form a triangle, their lengths must be related in a certain way. Notice that only one of the sets of segments below can form a triangle. The sum of the smallest two lengths must be greater than the greatest length.
Take Note Theorem 5-12: Triangle Inequality Theorem
The sum of the lengths of any two sides of a triangle is greater than the length of the third side.
You will prove Theorem 5-12 in Exercise 45.
Problem 4 Using the Triangle Inequality Theorem
Can a triangle have sides with the given lengths? Explain.
Think
How do you use the Triangle Inequality Theorem?
Test each pair of side lengths. The sum of each pair must be greater than the third length.
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3 ft, 7 ft, 8 ft
Yes. The sum of the lengths of any two sides is greater than the length of the third side.
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5 ft, 10 ft, 15 ft
No. The sum of 5 and 10 is not greater than 15. This contradicts Theorem 5-12.
✓ Got It?
- Can a triangle have sides with the given lengths? Explain.
- 2 m, 6 m, and 9 m
- 4 yd, 6 yd, and 9 yd
Table of Contents
- 6-1 The Polygon Angle-Sum Theorems
- 6-2 Properties of Parallelograms
- 6-3 Proving That a Quadrilateral Is a Parallelogram
- 6-4 Properties of Rhombuses, Rectangles, and Squares
- 6-5 Conditions for Rhombuses, Rectangles, and Squares
- 6-6 Trapezoids and Kites
- 6-7 Polygons in the Coordinate Plane
- 6-8 and 6-9 Coordinate Geometry and Coordinate Proofs