1. Bellringer Find the slope going through the points. Use the given information to write an equation for each line.  1.  2. (2, 3), (  1,  6)  1. m=-2/3  2.m=3  3. slope  1/3, y-intercept  2  4.  3. y=-1/3x-2  4.y=-3/2x+2

2. Geometry: Chapter 3 Parallel and Perpendicular lines

3. Connections

4. Lesson Purpose ObjectiveEssential Question  To use parallel lines to prove a theorem about triangles.  To find measures of angles of triangles.  How do the postulates and theorem for proving triangles congruent shorten the time and work involved?

5. Postulate 3-3 Parallel Postulate  Through any point not on a line, there is one and only one line parallel to the given line.  There is exactly one line through Parallel to m. P m

6. Triangle Angle-Sum Theorem 3-10  The sum of the measures of the angle of a triangle is 180.

7. Example #1 So we have  A+  B+  C=180 Using the angle measures we were given, we can substitute those values into our equation to get. 120+34+m  C=180 m  C=26 (1) Find the measure of ∠ C.. Using the diagram, we are given that m  A= 120 m  B=34

8. Example #2  (2) Find the value of x in the diagram below.  m  S=61  m  T=73  m  P=m  Q=x  m  S+m  T+m  SRT=180  61+73+m  SRT=180  m  SRT= 46   SRT  QRP thus,   QRP=46   P+  Q+46=180  x+x+46=180  2x+46=180   P=  Q=67

9. Key Concepts  The angle formed by one side of a triangle with the extension of another side is called an exterior angle of the triangle.

10. Key Concepts  Exterior angles get their name because they lie on the outsides of triangles.  The two angles that are not adjacent, or next to, the exterior angle of the triangle are called remote interior angles.

11. Triangle Exterior Angle Theorem 3-11  The Measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles.

12. Example #3 1) Find the measures of ∠ 1 and ∠ 2 in the figure below. Solution  m  S=42, and m  A=30  m  S+m  A+  1=180  42+30+  1=180  72+  1=180   1=108  m  S+m  A=  2  42+30=  2   2=72

13. Example #4 2) Find m ∠ B. Solution   R=93, and  JEB=132   B=9x+3   R+  B=  JEB  93+(9x+3)= 132  96+9x=132  9x=36  x=4   B=39

14. Real World Connections

15. Summary-Recap  The sum of the measures of the angles of a triangle is equal to 180.  The measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles.

16. Ticket Out and Homework Ticket OutHomework  pg.184-185 #s 10,14,20,24,25  What is true about the measures of angles in a triangle?  By the Triangle Angle Sum theorem, The sum of the measures of the angles of a triangle are equal to 180