DO NOW 1) X = 180 2) 55 + X = 180 3) X + 58 = 90 4) 31 + X = 90

Triangles, Triangles, and MORE Triangles Geometry Week 7 of 9 Unit 2: Angles and Angle Relationships 10/1 & 10/2

Standards & Objectives Standard 12.0 and 13.0 Objectives: To classify triangles and find the measures of their angles To use exterior angles of triangles

ACTIVITY Draw and cut out a large triangle. Draw and cut out a large triangle. Number the angles and tear them off. Number the angles and tear them off. Place the three angles adjacent to each other to form one angle. Place the three angles adjacent to each other to form one angle. 1)What kind of angle is formed by the three smaller angles? What is its measure? 2)Make a conjecture about the sum of the measures of the angles of a triangle.

Triangle Angle-Sum Theorem The sum of the measures of the angles of a triangle is 180. The sum of the measures of the angles of a triangle is 180.

Different Types of Triangles There are several different types of triangles. There are several different types of triangles. You can classify a triangle by its sides and its angles. You can classify a triangle by its sides and its angles. There are THREE different classifications for triangles based on their sides. There are THREE different classifications for triangles based on their sides. There are FOUR different classifications for triangles based on their angles. There are FOUR different classifications for triangles based on their angles.

Classifying Triangles by Their Sides EQUILATERAL – 3 congruent sides EQUILATERAL – 3 congruent sides ISOSCELES – at least two sides ISOSCELES – at least two sidescongruent SCALENE – no sides congruent SCALENE – no sides congruent

Classifying Triangles by Their Angles EQUIANGULAR – all angles are congruent EQUIANGULAR – all angles are congruent ACUTE – all angles are acute ACUTE – all angles are acute RIGHT – one right angle RIGHT – one right angle OBTUSE – one obtuse angle OBTUSE – one obtuse angle EQUIANGULAR ACUTE RIGHT OBTUSE

Can You Classify the Different Triangles in the Picture Below? Classify the following triangles: AED, ABC, ACD, ACE

The Classifications… Triangle AED = Equilateral, Equiangular Triangle AED = Equilateral, Equiangular Triangle ABC = Equilateral, Equiangular Triangle ABC = Equilateral, Equiangular Triangle ACD = Scalene, Obtuse Triangle ACD = Scalene, Obtuse Triangle ACE = Scalene, Right Triangle ACE = Scalene, Right So how did you do? So how did you do?

Triangle Exterior Angle Theorem The measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles. The measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles

EXAMPLE Measure of X = Measure of X = X

PRACTICE

EXAMPLE 113 = 70 + Measure of X 43 = Measure of X 113 X 70