6.3 Classifying Triangles Using the Pythagorean Theorem
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This document discusses classifying triangles using Pythagorean theorem and inequalities. It states that if a2 + b2 = c2, the triangle is right. If a2 + b2 > c2, the triangle is obtuse, and if a2 + b2 < c2, the triangle is acute. Examples are then given to classify triangles as right, obtuse or acute based on their side lengths.
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6.3 Classifying Triangles Using the Pythagorean Theorem
- 1. 6.3 More Classifying Triangles The student is able to (I can): • Use Pythagorean inequalities to classify triangles.
- 2. Converse of the Pythagorean Theorem If a2 + b2 = c2, then the triangle is a right triangle. Another way to think of this is Pythagorean Inequalities Theorem If then the triangle is an obtuseobtuseobtuseobtuse triangle. If then the triangle is an acuteacuteacuteacute triangle. 2 2 2 ,c a b> + 2 2 2 ,c a b< + 2 2 2 .c a b= +
- 3. Classifying Triangles right triangle obtuse triangle acute triangle 2 2 2 c a b> + 2 2 2 c a b< +2 2 2 c a b= + a b c a b c a b c
- 4. Examples Classify the following triangle measures as right, obtuse, or acute. 1. 5, 7, 10 2. 30, 16, 34 3. 3.8, 4.1, 5.2
- 5. Examples Classify the following triangle measures as right, obtuse, or acute. 1. 5, 7, 10 102 = 100, 52 + 72 = 74 ObtuseObtuseObtuseObtuse 2. 30, 16, 34 342 = 1156, 162 + 302 = 1156 RightRightRightRight 3. 3.8, 4.1, 5.2 5.22 = 27.04, 3.82 + 4.12 = 31.25 AcuteAcuteAcuteAcute