6.2 Classifying Triangles
- 1. Classifying Triangles The student is able to (I can): • Classify triangles by angles and by sides • Classify triangles using the Pythagorean Theorem
- 2. Classifying Triangles Triangles are classified by their side lengths and their angle measures as follows: • By side length – equilateral – all sides congruent (equal) – isosceles – two or more sides congruent – scalene – no sides congruent • By angle measure – acute – all acute angles – right – one right angle – obtuse – one obtuse angle – equiangular – all angles congruent
- 3. Practice Classify each triangle by its angles and sides. 1. 3. 2. 4. 90 110
- 4. Practice Classify each triangle by its angles and sides. 1. 3. 2. 4. 90 110 right scalene equiangular equilateral acute isosceles obtuse isosceles
- 5. 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 obtuse triangle. If then the triangle is an acute triangle. 2 2 2 ,c a b + 2 2 2 ,c a b + 2 2 2 .c a b= +
- 6. 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
- 7. 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
- 8. Examples Classify the following triangle measures as right, obtuse, or acute. 1. 5, 7, 10 102 = 100, 52 + 72 = 74 Obtuse 2. 30, 16, 34 342 = 1156, 162 + 302 = 1156 Right 3. 3.8, 4.1, 5.2 5.22 = 27.04, 3.82 + 4.12 = 31.25 Acute