1. California State Standards 1. Understand and Use undefined terms, axioms, theorems, and inductive and deductive reasoning 15. Use the Pythagorean Theorem 17. Prove theorems using coordinate geometry Lesson Goals Use the Segment Addition Postulate. Classify angles Use the angle addition postulate ESLRs: Becoming Competent Learners, Complex Thinkers, and Effective Communicators

2. Postulate (aka Axiom) a rule that is accepted as true without proof Theorem a rule that must be proven to be true.

3. This indicates that the points are collinear. Segment Addition Postulate If B is between A and C then AB + BC = AC ABC ABBC AC

4. Draw a sketch of the three collinear points, D, E, and F where D is between E and F. Write the Segment Addition Postulate for the 3 points. EFD

5. A B C D E x 9 35 x

6. The Distance Formula If A(x 1, y 1 ) and B(x 2, y 2 ) are points on a coordinate plane then the distance between A and B is x y A(x 1, y 1 ) B(x 2, y 2 ) C (x 1, y 2 )

7. x y The Distance Formula is closely related to the Pythagorean Theorem A B C c = AB c 2 = a 2 + b 2

8. Congruent Segments segments that have the same length A B X Y this represents a number equal to a number this represents a figure the same size and shape as another figure the symbol for congruent

9. Angle Two rays with a common initial point called the vertex The rays are called sides A B C A is the vertex of the angle the symbol for angle angles can also be named by a number placed in the interior of the angle. 3

10. Interior Exterior A Interior of an angle The points in the region between the sides of the angle. Exterior of an angle The points in the region NOT between the sides of an angle.

11. G D F C E Name the indicated angle

12. G D F C E Name a point in the interior of the angle.

13. G D F C E Name a point in the exterior of the angle.

14. G D F C E Name the indicated angle.

15. Name the indicated angle G D F C E

16. Angle Measurement The number of degrees in an arc between the sides of an angle. A B C

17. Congruent Angles Angles that have the same measure A P a number equal to a number figures the same size and shape

18. Angle Addition Postulate A P C B

19. C E F D

20. A B C G 120 o 35 o xoxo

21. Adjacent Angles Two angles that have a common vertex and side, but have no common interior points. Q R S P (angles that are next to each other) common vertex

22. Name all the pairs of adjacent angles. D A B C E

23. What is a postulate or axiom? If point B is between A and C, then what do we know about the points? Write the segment addition postulate for the points. When would the Distance Formula be used? In mathematics you don’t understand things. You just get used to them. – John von Neumann

24. Today’s Assignment  p. 21: 1 – 3, 11, 19, 20, 23 – 31  p. 30: 26 – 31, 39