Copy these into your Glossary TheoremExample Angle Sum Theorem The sum of the measures of the angles of a triangle is 180 m  W + m  X +m  Y = 180 Third Angle Theorem If two angles of one triangle are congruent to two angles of a second triangle, the third angles of the triangles are congruent. If  A  F and  B  D, then  C  E, then Exterior Angle Theorem The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles. m  YZP = m  X +m  Y CorollariesThe acute angles of a right triangle are complementary m  G + m  J = 90 There can be at most one right or obtuse angel in a triangle "It's okay to make mistakes. Mistakes are our teachers -- they help us to learn." John Bradshaw W X Y A B C D E F X Y S P G H J Acute

Chapter 4.2 Angles of Triangles: Objective: Understand and apply the angle sum and exterior angle theorems. Check.4.11 Use the triangle inequality theorems (e.g., Exterior Angle Inequality Theorem, Hinge Theorem, SSS Inequality Theorem, Triangle Inequality Theorem) to solve problems. Check.4.12 Apply the Angle Sum Theorem for polygons to find interior and exterior angle measures given the number of sides, to find the number of sides given angle measures, and to solve contextual problems. Spi.4.11 Use basic theorems about similar and congruent triangles to solve problems.

Angles of Triangle Cut out a triangle (1/2 size of a piece of paper) Label vertices A, B, and C (on front and back) Fold vertex B so it touches AC the fold line is parallel AC Fold A and C so they meet vertex B What do you notice about the sum of angles A, B and C? Tear of vertex A, and B Arrange  A and  B so they fill in the angle adjacent and supplementary to  C. What do you notice about the relationship  A and  B and the angle outside  C?

Demonstrated 2 Theorems TheoremExample Angle Sum Theorem The sum of the measures of the angles of a triangle is 180 m  W + m  X +m  Y = 180 Third Angle Theorem If two angles of one triangle are congruent to two angles of a second triangle, the third angles of the triangles are congruent. If  A  F and  B  D, then  C  E, then Exterior Angle Theorem The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles. m  YZP = m  X +m  Y CorollariesThe acute angles of a right triangle are complementary m  G + m  J = 90 There can be at most one right or obtuse angel in a triangle "It's okay to make mistakes. Mistakes are our teachers -- they help us to learn." John Bradshaw W X Y A B C D E F X Y S P G H J Acute

Angle Sum Theorem Given  ABC Prove: m  A+m  B+m  C = 180 Statement 1.  ABC 2.Line XY through A || CB 3.  1 and  CAY form a linear pair 4.  1 and  CAY are supplementary 5.m  1+m  CAY=180 6.m  CAY= m  2+m  3 7.m  1+m  2+m  3=  1   C,  3   B 9.m  1=m  C, m  3=m  B 10.m  C+m  2+m  B=180 Reasons 1.Given 2.Parallel Postulate 3.Def of linear pair 4.If 2  ’s form a linear pair, they are supplementary 5.Def of supplementary  ’s 6.Angle Addition Postulate 7.Substitution 8.Alternate Interior Angle Theorem 9.Def of congruent angles 10.Substitution C A B XY 1 2 3

Find the missing Angles 28  82  68  m  = 180 m  = 180 m  1 = 70 m  1 = m  2 vertical angles m  2 + m  = m  = 180 m  = 180 m  3 = 42

Find the missing Angles 74  43  79  m  = 180 m  = 180 m  1 = 63 m  1 = m  2 vertical angles m  2 + m  = m  = 180 m  = 180 m  3 = 38

Find the angle measures 50  78  120  m  1 = , exterior angle theorem 56  m  1 = 128 m  1 + m  2 = 180, linear pair are supplemental m  2 = 180 m  2 = 52 m  2 + m  3 = 120 exterior angle theorem 52+ m  3 = 120 m  3 = m  4 = 180, linear pair are supplemental m  4 = 60 m  = m  5 exterior angle theorem = m  5 116= m  5

Find the angle measures 41  64  38  m  1 =  m  1 = 70 m  1 + m  2 = 180, linear pair are supplemental m  2 = 110 m  2 = m  exterior angle theorem m  3= 110 – 64 = 46 m  3 + m  = m  = 180 m  4 = 102 m  4 + m  = m  = = m  5 29 

Right Triangle m  1 = 90 – 27 m  1 =  1

Practice Assignment Standard - page 248, Even Honors - Page – 44 Even