Triangle Inequalities and Theorems
Series of problems and theorems related to triangles, including inequalities and corollaries. Learn about properties of angles, sides, and lengths within a triangle, and apply theorems to solve geometric problems. Understand concepts like the relationship between angles and side lengths in triangles through visual representations.
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Presentation Transcript
5-6 Inequalities in One Triangle
Corollary to the Triangle Exterior Angle Theorem The measure of an exterior angle of a triangle is greater than the measure of each of its remote interior angles
Theorem 5-10 If two sides of a triangle are not congruent, then the larger angle lies opposite the longer side
Theorem 5-11 If two angles of a triangle are not congruent, then the longer side lies opposite the larger angle
Theorem 5-12 The sum of the lengths of any two sides of a triangle is greater than the length of the third side
Problem 4: Using the Triangle Inequality Theorem Can a triangle have side lengths with the given lengths? Explain.
Can a triangle have side lengths with the given lengths? Explain.
