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Bellwork Classify each angle as acute, obtuse or right 90o 72o 116o How do we know that angle 1 and angle 2 are congruent? 1 2 Apply Triangle Sum Properties Section 4.1 The Concept Today we’re going to recover some of the basics of triangles For most this should be review of some topics learned earlier in middle school The terminology used today will continue to be used throughout our study of triangles Triangle Definition There are two ways to describe triangles, by sides and by angles Definitions by side: Scalene: No sides are of equal lengths Isosceles: Two sides are of equal lengths Equilateral: All sides are of equal lengths Triangle Definition Definitions by angles: Acute: Containing three acute angles Right: Containing one right angle Obtuse: Containing one obtuse angle Equiangular: Containing three acute congruent angles Examples Classify these angles by both sides and angles Definitions Two important definitions for us in regards to triangles are: Interior Angles Exterior Angles Angles inside the triangle Angles formed by extending the sides of a triangle Important fact: An interior and it’s matching exterior angle form a linear pair Activity You are now getting a piece of paper, ruler and a triangle 1. Trace your triangle on the piece of paper 2. On you paper, draw a straight line that does not touch or intersect your triangle What does this 3. Sit quietly & patiently until everyone’s ready… tell us about the sum of the angles in a triangle? Theorems Theorem 4.1: Triangle Sum Theorem The sum of the measures of the interior angles of a triangle is 180o Activity Let’s do another activity with our triangles 1. Draw an exterior angle off of one of the corners of your traced triangle 2. Take the interior angle out of your torn pieces 3. Line the two angles up in the space provided What does this tell us about the sum of the other two angles in a triangle with relation to the third? Theorems Theorem 4.1: Triangle Sum Theorem The sum of the measures of the interior angles of a triangle is 180o Theorem 4.2: Exterior Angle Theorem The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles Corollary to Triangle sum Theorem The acute angles of a right triangle are complementary Examples Find the values of the angles 80 e 70 c d a b 25 80 Homework 4.1 1-7, 8-26 even, 27-34, 40-52, 55, 58, 62 Most Important Points Different kinds of Triangles by sides & angles Triangle Sum Theorem Exterior Angle Theorem