1. 1 Aim: What is the sum of angle measures in a triangle? Do Now: D E x y A B C z Given: Prove: StatementsReasons 1) 2) 3) 4) 5) 6) Given Def. straight angle Partition Postulate Substitution Post.

2. 2Geometry Lesson: Sum of Angles in a Triangle Theorem #19: The sum of the measure of the angles of a triangle is 180°. Corollary #19-1: If two angles of one triangle are congruent to two angles of another triangle, then the third angles are congruent. )) (( A E GC F B ((( Corollary #19-2: The acute angles of a right triangle are complementary. A B C

3. 3Geometry Lesson: Sum of Angles in a Triangle Corollary #19-3: Each acute angle of an isosceles right triangle measures 45°. Corollary #19-4: Each acute angle of an equilateral triangle measures 60°. A B C A B C

4. 4Geometry Lesson: Sum of Angles in a Triangle Corollary #19-5: The sum of the measures of the angles of a quadrilateral is 360°. A B C D

5. 5 Ex: Sum of Angle Measures in Triangles 1)In each case, state whether the 3 numbers can represent the angle measures of a triangle. a) 10, 120, 50 b) 65, 55, 65 c) 82, 14, 78 3) Find the measure of the largest angle of a triangle if it’s angle measures are in the ratio 1 : 3 : 5 4) The measure of the vertex angle of an isosceles triangle is 20 less than twice the measure of a base angle. Find the measures of all angles in the triangle.