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Triangles Chapter 4 B What is the sum of the angles inside a triangle? 180º? m 4 2 5 A 1 3 C Prove it AC m m ∠4 + m ∠2 + m ∠5 = 180° ∠1 ≅ ∠4 m ∠1 = m ∠4 and and Given Angle Addition Postulate/Definition of a Straight Angle ∠3 ≅ ∠5 Alternate Interior Angles Theorem m ∠3 = m ∠5 Definition of Angle Congruence m ∠1 + m ∠2 + m ∠3 = 180° Substitution Classifying Triangles by Sides Equilateral - Three congruent sides Isosceles - Two congruent sides Scalene - No congruent sides Classifying Triangles by Sides Find the values of x, y, and the measures of the sides of each triangle 4y − 1 y2 − 6 Equilateral - Three congruent sides 3y + 4 Isosceles - Two congruent sides 3x + 2 x2 + 4 x +3 Be ready to discuss these answers in class Classifying Triangles by Angles Acute - All three angles < 90º Equiangular - All three angles = 60º Right - One right angle Obtuse - One obtuse angle Exterior Angle Theorem (you’ll be proving this) The measure of an exterior angle of a triangle is equal to the sum of the measures of its remote interior angles Remote Interior Angles 2 m ∠4 = m ∠1 + m ∠2 1 3 4 Third Angle Theorem If two angles of one triangle are congruent to two angles of another triangle, then the third pair of angles are congruent. P B Q A C R ∠A ≅ ∠P ∠B ≅ ∠Q If this is true then ∠C ≅ ∠R Third Angle Theorem If two angles of one triangle are congruent to two angles of another triangle, then the third pair of angles are congruent. P 61º B (9x2)º A 61º (27x)º C Q R Find the values of x, m ∠C , m ∠R , m ∠B , and m ∠Q Be ready to discuss these answers in class