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

Classify the Triangle by Its Angles and Sides

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

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

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 Linear Pair Postulate