1. Parallel Lines and Triangles
Skill 18

2. Objective
HSG-CO.10: Students are responsible for using parallel lines to prove theorems about triangles and finding measures of the angles of triangles.

3. Postulate 11
Parallel Postulate
Through a point not on a line, there is one and only one line parallel to the given line. P l

4. Theorem 16
Triangle Angle-Sum Theorem
The sum of the measures of the angles of a triangle is 180. B A C
If ∆𝑨𝑩𝑪
Then 𝒎∠𝑨+𝒎∠𝑩+𝒎∠𝑪=𝟏𝟖𝟎

5. Theorem 16; Triangle Angle-Sum Theorem
Given: ∆𝐴𝐵𝐶 Prove: 𝑚∠𝐴+𝑚∠2+𝑚∠𝐶=180
Statement Reason
1) ∆𝐴𝐵𝐶
1) Given
2) Draw 𝑃𝑅 through B, so that 𝑃𝑅 ∥ 𝐴𝐶 .
2) Parallel Postulate
3) 𝑚∠𝑃𝐵𝐶 𝑎𝑛𝑑 𝑚∠3 are supplementary
3) Linear Pair Postulate
4) Def. of Supplementary
4) 𝑚∠𝑃𝐵𝐶+𝑚∠3=180
5) Angle Addition Postulate
5) 𝑚∠𝑃𝐵𝐶=𝑚∠1+𝑚∠2

6. Theorem 16; Triangle Angle-Sum Theorem
Given: ∆𝐴𝐵𝐶 Prove: 𝑚∠𝐴+𝑚∠2+𝑚∠𝐶=180
Statement Reason
6) 𝑚∠1+𝑚∠2+𝑚∠3=180
6) Substitution
7) ∠1≅∠𝐴 and ∠3≅∠𝐶
7) Alt. Int. Angle Theorem
8) 𝑚∠1=𝑚∠𝐴 and 𝑚∠3=𝑚∠𝐶
8) Def. of Congruent Angles
9) 𝑚∠𝐴+𝑚∠2+𝑚∠𝐶=180
9) Substitution
Q.E.D.

7. Theorem 17 B Remote Interior 2 Exterior 1 3 C A
Triangle Exterior Angle Theorem
The measure of each exterior angle of a triangle equal the sum of the measures of the remote interior angles. B A C 2 3
Remote Interior 1
Exterior
If ∆𝑨𝑩𝑪
Then 𝒎∠𝟏=𝒎∠𝟐+𝒎∠𝟑

8. Definitions
An exterior angle of a triangle is an angle formed by a side and an extension of an adjacent side.
For each exterior angle of a triangle, the nonadjacent interior angles are its remote interior angles.

9. #18: Parallel Lines and Triangles
Questions?
Summarize Notes
Homework
Video
Quiz