1. Parallel Lines and the Triangle Angle-Sum Theorem
Geometry
Mrs. King
Unit 3, Lesson 3

2. Theorem 2-1 Triangle Angle-Sum Theorem
The sum of the measures of the angles of a triangle is 180.

3. Video: Sum of the Angles of a Triangle

4. Find the measure of the missing angle x x

5. Practice
Find all Variables:

6. Practice
Find all Variables:

7. Practice
Find all variables

8. Definition
Exterior Angle: an angle formed by the side of a polygon and an extension of a side.

9. Definition
Remote Interior Angle: the two nonadjacent interior angles to an exterior angle.

10. Theorem 2-2 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. Find the measure of the missing angle

12. Find the measure of the missing angle

13. Definition
Corollary: a statement that follows directly from a theorem.

14. Corollary to Theorem 2-2
The measure of an exterior angle of a triangle is greater than the measure of either of its remote interior angles.

15. Types of Triangles (by sides)
Equilateral
Isosceles
Scalene

16. Equilateral Triangles
Definition:
A triangle with three congruent sides.
Example:

17. Isosceles Triangles Definition: Example:
A triangle with two congruent sides.
Example:

18. Scalene Triangles Definition: Example:
A triangle with no congruent sides.
Example:

19. Types of Triangles (by angle)
Equiangular
Acute
Right
Obtuse

20. Equiangular Triangles
Definition:
A triangle with three congruent angles.
Example:

21. Acute Triangles Definition: Example:
A triangle whose angles are all acute.
Example:

22. Right Triangles
Definition:
A triangle with one right angle.
Example:

23. Obtuse Triangles Definition: Example:
A triangle with one obtuse angle.
Example:

24. Classify the triangle by its sides and its angles.
The three sides of the triangle have three different lengths,
so the triangle is scalene.
One angle has a measure greater than 90, so the triangle is obtuse.
The triangle is an obtuse scalene triangle.