2.  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

3.  The sum of the angles of a triangle is 180
degrees

4.  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

5.  Through a point not on a line, there is one
and only one line parallel to the given line.

6.  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.

7.  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

8.  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.

9.  What are the values of x, y, and z?
 X = 102
 Y = 78
 Z = 66

10.  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

11.  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

12. <1 = 46 + 41 =87

13. 53 + <2 = 119
<2 = 66

14. X = 50

15.  Pg. 175-177
 9-18 (3s), 20, 21, 25, 26, 32, 34
 10 problems