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Aim: What is the sum of angle measures in a triangle? Do Now: Given: DBE || AC Prove: mA my mC 180 Statements 1) DBE || AC 2) mDBE 180 B x y z D A E C Reasons 1) Given 2) Def. straight angle 3) mDBE mx my mz 3) Partition Postulate 4) mx my mz 180 5) mx mA, mz mC 4) Substitution Post. 5) If || lines are cut by a 6) mA my mC 180 transv., alt. int. 's are . 6) Substitution Post. 1 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. B F C A G E If A E, and C G, then ...B F . Corollary #19-2: The acute angles of a right triangle are complementary. B If ABC is a right triangle and C mC 90, then mA mB ...90. A Geometry Lesson: Sum of Angles in a Triangle 2 Corollary #19-3: Each acute angle of an isosceles right triangle measures 45°. B C A If ABC is an isosceles right triangle, then mA mB ... 45 Corollary #19-4: Each acute angle of an equilateral triangle measures 60°. C If ABC is an equilateral trianlge, then mA mB mC ...60. A B Geometry Lesson: Sum of Angles in a Triangle 3 Corollary #19-5: The sum of the measures of the angles of a quadrilateral is 360°. C Given quadrilateral ABCD, mA mB mC mD ... 360 D A B Geometry Lesson: Sum of Angles in a Triangle 4 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 2) In EFG, EF FG. If mE 48, determine the measures of F and G. 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. 5) The degree measures of a triangle are represented by 4 x 10, 2 x 5, and 3x 5. Show that the triangle 5 is a right triangle.