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Classify These Triangles by Sides and Angles Chapter 4 Congruent Triangles Section 4.1: Triangle Sum Properties Todays Objective: Determine if a right triangle can be an obtuse triangle and explain why or why not. Triangle Classifications By Sides: • Equilateral Triangle – All sides have the same length By Angles: • Equiangular Triangle – All internal angles have the same measure Triangle Classifications What do we call a polygon that is both equilateral and equiangular? Regular Polygon What is the sum of the measures of the interior angles of any triangle? Theorem 4.1: Triangle Sum Theorem The sum of the measures of the interior angles of any triangle is 180° Triangle Classifications By Sides: • Isosceles Triangle – Two sides have the same length By Angles: • Acute Triangle – All internal angles are acute. Triangle Classifications By Sides: • Scalene Triangle – All sides have different lengths By Angles: • Obtuse Triangle – One internal angle is obtuse Triangle Classifications By Sides: • Scalene or Isosceles Triangle – At least one side (the hypotenuse) must be longer than the other two. By Angles: • Right Triangle – One internal angle is a Right Angle (measures 90°) Angle Measures The measure of angle d must be equal to what? 𝒎<𝒅=? Angle d and Angle c are a ___________ 𝒎<𝒅=𝒎<𝒂+𝒎<𝒃 b a c d Theorem 4.2 Exterior Angle Theorem • The measure of the exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles Right Triangles Can a right triangle ever be an obtuse triangle? B 𝟗𝟎° + 𝒎 < 𝑨 + 𝒎 < 𝑩 = 𝟏𝟖𝟎° A The Acute angles of a Right Triangle must be Complementary. Homework Section 4.1 p.221 # 1 - 7, 15 – 17, 21 – 26