Section 3.3 Triangles Thompson. Triangle Sum Theorem The sum of the measures --?--.

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Presentation transcript:

Section 3.3 Triangles Thompson

Triangle Sum Theorem The sum of the measures --?--.

The triangle angle sum theorem The sum of the measures of the angles of a triangle is 180. m<A + m<B + m<C = 180 A B C

83˚ 45˚ x˚x˚ Find the value Of x

( 4x+7 )˚ (8x-1) ˚ Find the value Of x

Types of Triangles Equilateral – All sides congruent Isosceles – At least two sides are congruent Scalene – No sides are congruent “By Sides” Page 133

Types of Triangles “By Angles” Equiangular – All angles are congruent Acute – All angles are acute (less than 90) Right – One right angle (90 ) Obtuse – One obtuse angle (more than 90 less than 180)

Classifying Triangles

Now we’re going to practice “classifying triangles” Both by “Sides” and by “Angles”

By Angles equiangular By Sides equilateral

By Angles “Right” By Sides “Scalene”

By Sides “Isosceles” By Angles “Acute”

By Angles “Obtuse” By Sides Isosceles

Definition: Exterior Angles of Triangle Exterior Angle – The angle formed by a side and an extension of the side Remote Interior Angle – The two non-adjacent interior angles Exterior Angle Remote Interior Angles

Interior vs. Exterior Angles interior exterior All the angles inside the triangle are called interior angles. If you extend the sides of the triangle, then the angles that form a linear pair with the interior angles are called exterior angles.

Exterior Angle Theorem The measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles. m<1 = m<2 + m<

115˚ y˚ 52˚ x˚x˚

The measure of an exterior angle of a triangle is greater than the measure of either of its remote interior angles. m m m< Corollary (free postulate)

SAT Example Find the values of a, b, and c.

SAT Example What is the value of c?

“…This is pointless, when am I ever Going to run into a triangle in real life?!...”

Classwork , 16-23, 31-36