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Angles and triangles.notebook October 03, 2016 Section 34 Angles of Triangles What is a triangle? 1 Angles and triangles.notebook October 03, 2016 Triangles • Definition • A figure where three segments join at three points • Vertex • Sides 2 Angles and triangles.notebook October 03, 2016 Classifying or Describing Triangles • Sometimes by the number of congruent SIDES • Sometimes by the its ANGLES 3 Angles and triangles.notebook October 03, 2016 Classifying by Sides • • • • • • Scalene triangle No congruent sides Isosceles triangle At least two congruent sides Equilateral triangle All sides congruent 4 Angles and triangles.notebook October 03, 2016 Classifying by Angles • Acute • Obtuse • Right • • • • Three acute angles One obtuse angle One right angle All congruent angles • Equiangular 5 Angles and triangles.notebook October 03, 2016 Side Note • Often diagrams needed for proofs are lacking elements. • If this is the case an AUXILIARY LINE (or ray or segment) can be drawn to help with the proof. • AUXILIARY LINES are denoted using a dotted/dashed line. 6 Angles and triangles.notebook October 03, 2016 Theorem 311 The sum of the measures of the angles of a triangle is 180. 7 Angles and triangles.notebook October 03, 2016 Practice Find the missing angle then state whether the triangles are acute, obtuse or right • • • • • 1. 55, 43 2. 47,43 3. 80,75 4. 33, 33 5. 24, 66 8 Angles and triangles.notebook October 03, 2016 Now that we have theorem 311 What can be said about equiangular triangles? 9 Angles and triangles.notebook October 03, 2016 Corollary 2 Each angle of an equiangular triangle is 60°. Draw me a equiangular triangle. 10 Angles and triangles.notebook October 03, 2016 Using theorem 311 Can a triangle have two angles greater than or equal to 90°? Draw me a triangle with two obtuse angles? Can it be done? What about with two right anlges? 11 Angles and triangles.notebook October 03, 2016 Corollary 3 In a triangle, there can be at most one right or obtuse angle. 12 Angles and triangles.notebook October 03, 2016 Using theorem 311 In a right triangle what can be said about the two other angles? Draw me a right triangle and make a conclusion about the other two angles. 13 Angles and triangles.notebook October 03, 2016 Corollary 4 The acute angles of a right triangle are complementary. 14 Angles and triangles.notebook October 03, 2016 Corollary 1 If two angles of one triangle are congruent to two angles of another triangle, then the third angles are congruent. 15 Angles and triangles.notebook October 03, 2016 Theorem 312 The measure of an exterior angle of a triangle equals the sum of the measures of the two remote interior angles. 16 Angles and triangles.notebook October 03, 2016 CE on p.96 Homework:Written exercises pg 97 #118 17