n Bellwork Classify each angle as acute obtuse

n Bellwork Classify each angle as acute, obtuse or right n n 90 o 72 o 116 o How do we know that angle 1 and angle 2 are congruent? 1 2

Apply Triangle Sum Properties Section 4. 1

The Concept n n n 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: n Scalene: No sides are of equal lengths n Isosceles: Two sides are of equal lengths n Equilateral: All sides are of equal lengths

Triangle Definitions by angles: n Acute: Containing three acute angles n Right: Containing one right angle n Obtuse: Containing one obtuse angle n 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: n Interior Angles n n Exterior Angles n n Angles inside the triangle Angles formed by extending the sides of a triangle Important fact: n 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 180 o

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 180 o 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