Chapter 4 Section 4.1 – Part 1 Triangles and Angles

Warm-Up

Definition of a Triangle Triangle: () A figure formed by three segments joining three non-collinear points

Parts of a Triangle Vertex Interior Angle Side Exterior Angle

Classifying Triangles by Sides Equilateral  3 congruent Sides Isosceles  At least 2 congruent Sides Scalene  No Sides congruent

Special Vocabulary in Isosceles Triangles Legs A B C ABC is isosceles are the legs Two Congruent Sides is the base The “other” side Base

Classifying Triangles by Angles Equiangular  3 congruent Angles Acute  All Angles are Acute Right  One Right Angle Obtuse  One obtuse Angle

Special Vocabulary in Right Triangles D E F DEF is a right  are the legs Two Perpendicular Sides Legs is the Hypotenuse The side opposite the right angle Hypotenuse

Hyp Leg Base

Classify the Triangle by Its Angles and Sides Acute/Isosceles Right/Scalene Equilateral/Equiangular Obtuse/Scalene Right/Scalene Obtuse/Isosceles

Classify the Sentence With Always, Sometimes, or Never An equilateral triangle is _____ an isosceles triangle Always An isosceles triangle is _____ an equilateral triangle Sometimes A right triangle is _____ an acute triangle Never An exterior angle of a triangle is _____ acute

Triangle Sum Theorem Inductive reasoning Triangle Sum Theorem: The sum of the measures of the angles of a triangle is 180° mA + mB + mC = 180°

Find the Measure of the Numbered Angle Triangle Sum Theorem m1 + 42 + 90 = 180 m1 + 132 = 180 m1 = 48

Corollary to the Triangle Sum Theorem Corollary: A statement that can be easily proven using the theorem. Inductive reasoning Corollary to the triangle sum theorem: the acute angles of a right triangle are complementary. mA + mC = 90

Find the Measure of the Numbered Angle Corollary Triangle Sum Theorem m1 + 53 = 90 m1 = 37 m2 + 33 = 90 m2 = 57

Exterior Angle Theorem Inductive Reasoning Exterior Angle Theorem: The measure of an exterior angle of a triangle is equal to the sum of the two nonadjacent interior angles mA + mB = mBCD

Find the Measure of the Numbered Angle Exterior Angle Theorem m1 + 68 = 102 m1 = 34 Linear Pair Postulate m2 + 102 = 180 m2 = 78