3 3 Parallel Lines and the Triangle Sum

3 -3 Parallel Lines and the Triangle Sum Theorem L. E. Q. How do you find measures of interior and exterior angles of triangles?

Investigation: The Sum of the Angles of a Triangle. � Draw and cut out a large triangle. � Number the angles and tear them off. � Place three angles adjacent to each other to form one angle. § What do you see?

If you add up the measures of the interior angles of a triangle, What is the total? 65º 25º Focus – Prove the Triangle Sum Theorem

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

Applying the triangle sum theorem. �Find the missing angle. 47º

Using algebra. � Find the values of x, y, and z. G 21 39 F x - 11 x y J z H

Classifying a triangle by its angles:

Equiangular Triangle � All 3 angles are congruent.

Right Triangles � Has one right angle.

Acute Triangle � First � An tell me this, what is an acute angle? acute triangle has three acute angles. 50° 46° 72° 50° 58° 84°

Obtuse Triangle � What’s � An an obtuse angle? obtuse triangle has one obtuse angle. X S A 135° W 98° M V

Scalene Triangle �A triangle with no congruent sides. X 11” 28” W V 20” Can we use tick/dash marks to denote congruence of sides in triangle XWV?

Equilateral Triangle � An equilateral triangle has three congruent sides. 3’ 3’ 3’

Isosceles Triangle � Has at least two congruent sides. F J M E A O

What is an exterior angle of a polygon? � An angle that is formed outside the polygon by extending a side of the polygon past its vertex.

What are remote interior angles? � The 2 interior angles of a triangle that are nonadjacent to the exterior angle.

Triangle Exterior Angle Theorem. � The measure of each exterior angle of a triangle is equal to the sum of the 2 remote interior angles. Add These! Get This!

What is the measure of Angle T, U, J, and L? T 55º J U 120º L

Homework: � Pg 134 – 135 #s 1 -15, 24 -28 all.