1. Triangles: Angle Sum & Classifying Triangles Tutorial 12b

2. The Triangle Angle-Sum Theorem The interior angles of any triangle have a sum of 180 . A B C m  A + m  B + m  C = 180

3. Example Problems: Find the missing angles. xx 33  117  x =180 – (117 + 33) ww tt 30  t = w = 60  y = z = 88  92  zz 47  45  yy =30 

4. Exterior Angles of a Triangle An exterior angle of a polygon is an angle formed by a side and an extension of a side. For each exterior angle of a triangle, the two non-adjacent interior angles are called its remote interior angles. 3 1 2 Remote Interior Angles are Exterior Angle is 11  2 and  3

5. Exterior Angle Theorem The measure of an exterior angle of a triangle equals the sum of the measures of its two remote interior angles. 2 31 m  1 = m  2 + m  3

6. Corollary: Exterior Angle Theorem The measure of an exterior angle of a triangle is greater than the measure of either of its remote interior angles. 2 31 m  1 > m  2 and m  1 > m  3

7. Classifying Triangles: By Side Lengths Equilateral All sides congruent Isosceles At least two sides congruent Scalene No sides congruent

8. Classifying Triangles: By Angle Measure Equiangular All angles congruent Acute All angles acute Obtuse One obtuse angle Right One right angle If you cannot remember the types of angles click here. Review

9. A little more about Right Triangles In a right triangle, the side opposite the right angle is the longest side. It is the called the hypotenuse. The other two sides are called the legs of a right triangle. b c a Side c is the hypotenuse, and is the longest side. Sides a and b are the legs of the triangle.

11. Angles less than 90° are called Acute Angles. Angles equal to 180° are called Straight Angles. Angles equal to 90° are called Right Angles. Classifying Angles Acute Angle: Obtuse Angle: Right Angle:Straight Angle: Types of Angles: Angles greater than 90° are called Obtuse Angles. Symbol for right angle 180° Back