1. Lesson 3: (3.4) Parallel Lines and the Triangle Angle-Sum Theorem

2. What are we learning?
Purpose: Students will classify triangles, find the measures of their angles, and use exterior angles of triangles to solve problems.
Evidence Outcome: Prove geometric theorems (lines, angles, triangles, parallelograms).
Purpose (Relevancy): This concept is used to find the reclining angle of a lazy boy chair.

3. Finding Angle Measures in TrianglesC
50°
35° A B
Theorem 3-12: Triangle Angle-Sum Theorem:
The sum of the measures of the angles of a triangle is 180.

4. Finding Angle Measures in TrianglesC
50°
35° A B
Find the measure of the three angles. Justify your work.

5. Finding Angle Measures in Triangles
Find the values of x, y, and z. Justify your work.
39°
21°
65° x° y° z° F J H

6. Finding Angle Measures in TrianglesB
Find the values of x, y, and z. x° y°
62° z°
49° A C D

7. Classifications of Triangles
Equiangular
Acute
Right
Obtuse
Equilateral
Isosceles
Scalene

8. Classifications of Triangles
Classify the following triangles by their angles and sides.
3 in.
4 in.
5 in.
7 cm.
16 cm.
106°
37°
Draw an equilateral right triangle.
NOT POSSIBLE!!!

9. Using Exterior Angles of Triangles
Exterior Angle of a Polygon: An angle formed by a side and an extension of an adjacent side.
Remote Interior Angles
Exterior Angle 1 2 3
Remote Interior Angles: The two nonadjacent interior angles corresponding to each exterior angle of a triangle.

10. Using Exterior Angles of Triangles1 2 3
Theorem 3-13: 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.

11. Using Exterior Angles of Triangles
100° x°
50°
Find the measure of the x. Justify your work.

12. Using Exterior Angles of Triangles
Find the values of w, x, y, and z.
97° x° y°
53° w°
86° z°

13. Little More Practice
Find the value of x.
(80 – 2x)°
(70 – 3x)°

14. and the Triangle Angle-Sum Theorem
(3.4): Parallel Lines
and the Triangle Angle-Sum Theorem
HOMEWORK: (3.4): Pgs ; 2-26 even, 32, 34, 40
Homework Quiz Next Class!
TERMS: equiangular Δ, acute Δ, right Δ, obtuse Δ,
equilateral Δ, isosceles Δ, scalene Δ.
Remember, with great power, comes great responsibility.
-Uncle Ben