Entry Task Cut out a large triangle. Use a straight edge and make it NEAT What is the sum of the measures of the 3 angles? Do not use a protractor! Not sure? Use the blue box on pg. 171 Even if you know the answer, SHOW ME why.

Parallel Lines and Triangles 3.5 Learning Target I understand the sum of the measure of the angles of a triangle and how it relates to an exterior angle

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Use the diagram drawn from the information collected to find m  XYZ. Example 1A: Application m  XYZ + m  YZX + m  ZXY = 180° Sum. Thm m  XYZ = 180 Substitute 40 for m  YZX and 62 for m  ZXY. m  XYZ = 180 Simplify. m  XYZ = 78° Subtract 102 from both sides.

Use the diagram drawn from the information collected to find m  YXW. Example 1B: Application m  YXZ + m  WXY = 180° Lin. Pair Thm. and  Add. Post m  WXY = 180 Substitute 62 for m  YXZ. m  WXY = 118° Subtract 62 from both sides. Step 1 Find m  WXY. 118°

Use the diagram drawn from the information collected to find m  YWZ. Example 1B: Application Continued Step 2 Find m  YWZ. 118° m  YWX + m  WXY + m  XYW = 180° Sum. Thm m  YWX = 180 Substitute 118 for m  WXY and 12 for m  XYW. m  YWX = 180 Simplify. m  YWX = 50° Subtract 130 from both sides.

Vocabulary Auxilary Line Remote interior Angle Exterior angle

The interior is the set of all points inside the figure. The exterior is the set of all points outside the figure. Interior Exterior

An interior angle is formed by two sides of a triangle. An exterior angle is formed by one side of the triangle and extension of an adjacent side. Interior Exterior  4 is an exterior angle.  3 is an interior angle.

Each exterior angle has two remote interior angles. A remote interior angle is an interior angle that is not adjacent to the exterior angle. Interior Exterior  3 is an interior angle.  4 is an exterior angle. The remote interior angles of  4 are  1 and  2.

Discover…. Can you find a relationship between angle 4 and any of the other angles shown?

An auxiliary line is a line that is added to a figure to aid in a proof. An auxiliary line used in the Triangle Sum Theorem Try this: Using an auxiliary line, prove that the sum of the 3 angles of a triangle is 180. StatementReason 1)Line L // AC1) Given 2)<4+<2+<5 = 1802) Linear Trio 3) <1=<4 and <3=<53) AIA 4) <1+<2=<3=1804) sub

Triangle Ratios A triangle has an angle measure of 80 degres. The other two angles have a ratio of 2 to 3. Find the other angle measures. 80 What do we put here?

Homework Homework –p odds, 29 and 31 Challenge - 36

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