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Angle Relationships in Triangles April 24, 2013 What's Going On? What Do We Know? SATT, SAT, EAT Exit Card Learning Goal I will be able to determine and describe the properties and relationships of the interior and exterior angles of triangles. 1 Angle Relationships in Triangles April 24, 2013 Unit 5: Geometric Relationships Today's Topic Angle Relationships in Triangles 2 Angle Relationships in Triangles April 24, 2013 What Do We Know? 3 Angle Relationships in Triangles April 24, 2013 What Do We Know? 4 Angle Relationships in Triangles April 24, 2013 What Do We Know? one set of parallel sides 5 Angle Relationships in Triangles April 24, 2013 What Do We Know? a b b a opposite 6 Angle Relationships in Triangles April 24, 2013 What Do We Know? alternate corresponding co-interior 180o 7 Angle Relationships in Triangles April 24, 2013 What Do We Know? What is the sum of the angles in a triangle? o 180 8 Angle Relationships in Triangles April 24, 2013 What is the sum of the angles in a triangle? o 180 ALWAYS This is actually a theorem... our first theorem! The Sum of the Angles in a Triangle Theorem (SATT) The sum of the interior angles of any triangle is always 180o. 9 Angle Relationships in Triangles April 24, 2013 Theorems Sum of the Angles in a Triangle Theorem (SATT) Find the measure of angle X. To find the measure of an interior angle given two interior angles: 23o X 39o 1. Start with 180o. 2. Subtract each angle. 3. What remains is the measure of the missing angle. 10 Angle Relationships in Triangles April 24, 2013 Theorems Supplementary Angle Theorem (SAT) What's are supplementary angles? A supplementary angles are two angles that exist along a straight line X B Y Z C A and X B and Y C and Z 11 Angle Relationships in Triangles April 24, 2013 Theorems Supplementary Angle Theorem (SAT) supplementary angles are two angles that exist along a straight line A X What is the sum of two supplementary angles? B Y Z C 12 Angle Relationships in Triangles April 24, 2013 Theorems Supplementary Angle Theorem (SAT) The sum of two supplementary angles is 180o. A X A + X = 180o B + Y = 180o C + Z = 180o B Y Z C 13 Angle Relationships in Triangles April 24, 2013 Theorems What about the exterior angles of a triangle? A X B Y Z C 14 Angle Relationships in Triangles April 24, 2013 A X We know that 180o 180o 180o (A + X) + (B + Y) + (C + Z) = 540o SAT SAT SAT B Y Z C AND X + Y + Z = 180o SATT So... A + X + B + Y + C + Z = 540o If we remove X, Y and Z we are taking away 180o worth of angles. What do we have left? We only have A, B and C left (the exterior angles!) And we have to take 180o from 540o... 540o - 180o = 360o 15 Angle Relationships in Triangles April 24, 2013 Theorems The Exterior Angle Theorem (EAT) The sum of the exterior angles of a triangle is always 360o. A X A + B + C = 360 B Y o Z C 16 Angle Relationships in Triangles April 24, 2013 Exit Question Find the measure of angle x. State any and all theorems you use. D A x E 67o 29o B C F 17 Angle Relationships in Triangles April 24, 2013 18 Angle Relationships in Triangles April 24, 2013 19