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Bellringer

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. Geometry: Chapter 3 Parallel and Perpendicular lines .

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Bellringer

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  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 3-5 Parallel Lines and Triangles

  3. Connections

  4. Lesson Purpose Objective Essential 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 (1) Find the measure of ∠C. • 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 . 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 Out Homework • 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

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