Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Multilateration wikipedia , lookup
Noether's theorem wikipedia , lookup
Integer triangle wikipedia , lookup
Rational trigonometry wikipedia , lookup
History of trigonometry wikipedia , lookup
Perceived visual angle wikipedia , lookup
Euler angles wikipedia , lookup
Trigonometric functions wikipedia , lookup
Geometry Notes Section 4-2 What you’ll learn. . . . How to apply the angle sum theorem How to recognize exterior angles and apply the exterior angle theorem Vocabulary Exterior angle of a triangle Remote interior angles Third angle theorem The Angle Sum Theorem Consider the sum of the angles of a triangle. . . . The sum of the measures of the angles of a triangle will always be 180° Example #1:Determine the angle measures. Example #2:Determine the angle measures. Example #3:Determine the angle measures Example #4:Determine the angle measure The Exterior Angle Theorem 2 4 1 3 Exterior Angles will always make a linear pair with an interior angle of a triangle. Each exterior angle will be associated with 2 remote interior angles (the two angles not connected to that exterior angle). The exterior angle theorem: Exterior angles and their remote interior angles share a special relationship. The measure of an exterior angle of a triangle will always be equal to the sum of the measures of its remote interior angles. Example Problem #5: Find x and y. The Third angle Theorem 5 4 6 2 1 3 If two angles of one triangle measure the same as two angles from another triangle, their third angles must also be the same measure. Example Problem #6: Find x and y. Have you learned. . . . How to apply the angle sum theorem How to recognize exterior angles and apply the exterior angle theorem Assignment: Non-Proof: Worksheet 4-2 Proof: p.189 (15-38); all diagrams must be drawn in your homework