Geo 3-5 Parallel Lines and Triangles

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Geo 3-5 Parallel Lines and Triangles

  1. 1.  Students will be able to: ◦ Find measures of angles of triangles ◦ Use parallel lines to prove theorems about triangles ◦ Define and apply the triangle sum and triangle exterior angle theorems
  2. 2.  The sum of the angles of a triangle is 180 degrees
  3. 3.  List some things you know about triangles The sum of the angles add to be 180 There are obtuse, acute, and right triangles There are scalene, equilateral, and isosceles triangles In a right triangle, the two acute angles add to be 90 degrees
  4. 4.  Through a point not on a line, there is one and only one line parallel to the given line.
  5. 5.  Sometimes when proving things we need to add lines to the diagram. Auxiliary Line: a line you add to a diagram to help explain relationships in proofs. In the picture below the red line was added to help with the following proof.
  6. 6.  Statements  Reasons 1. ΔABC  1. Given 2. Draw line PR through B,  2. Parallel Postulate parallel to AC 3.<1, <2, <3 are Suppl  3. Def. of Linear Pairs  4. Def. of Suppl. <s 4.<1 + <2 + <3 = 180  5. Alt. Interior Angles 5. <1 ≅<A, <3 ≅<C 6. m<1 = m<A, m<3 = m<C  6. Def. of Congruence 7. m<A + m<2 + m<C = 180  7. Substitution
  7. 7.  The sum of the measures of the angles of a triangle is 180. If you know the measures of two angles of a triangle, you can use this theorem to find the third measure.
  8. 8.  What are the values of x, y, and z? X = 102 Y = 78 Z = 66
  9. 9.  Exterior Angle of a Polygon ◦ An angle formed by a side and an extension of an adjacent side. Remote Interior Angles ◦ The two nonadjacent interior angles to the exterior angle Below <1 is the exterior angle, <2 and <3 are the remote interior angles
  10. 10.  The measure of the exterior angle equals the sum of the two remote interior angles. mExterior Angle = Remote Int. + Remote Int m<1 = m<2 + m<3
  11. 11. <1 = 46 + 41 =87
  12. 12. 53 + <2 = 119<2 = 66
  13. 13. X = 50
  14. 14.  Pg. 175-177 9-18 (3s), 20, 21, 25, 26, 32, 34 10 problems

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