Ch. 1

1. Ch. 1

2. B 3 3 P A Midpoint of a segment • The point that divides the segment into two congruent segments.

3. B 3 3 P A Bisector of a segment • A line, segment, ray or plane that intersects the segment at its midpoint.

4. Bisector of an Angle • The ray that divides the angle into two congruent adjacent angles (pg 19)

5. More Definitions • Intersect – Two or more figures intersect if they have one or more points in common. • Intersection – All points or sets of points the figures have in common.

6. When a line and a point intersect, their intersection is a point. l B

7. When 2 lines intersect, their intersection is a point.

8. When 2 planes intersect, their intersection is a line.

9. When a line and plane intersect, their intersection is a point.

10. A B C Segment Addition Postulate • If B is between A and C, then AB + BC = AC.

11. Angle Addition Postulate • If point B lies in the interior of  AOC, • then m  AOB + m  BOC = m  AOC. • What is the interior of an angle? If  AOC is a straight angle and B is any point not on AC, then m  AOB + m  BOC = 180. Why does it add up to 180?

12. Ch. 2

13. Conditional: is a two part statement with an actual or implied if-then. The If-Then Statement If p, then q. p ---> q hypothesis conclusion If the sun is shining, then it is daytime.

14. Circle the hypothesis and underline the conclusion If a = b, then a + c = b + c

15. Other Forms • If p, then q • p implies q • p only if q • q if p Conditional statements are not always written with the “if” clause first. All of these conditionals mean the same thing. What do you notice?

16. Properties of Equality Numbers, variables, lengths, and angle measures

18. Properties of Congruence Segments, angles and polygons

19. Complimentary Angles Any two angles whose measures add up to 90. If mABC + m SXT = 90, then  ABC and  SXT are complimentary. S A  ABC is the complement of  SXT  SXT is the complement of  ABC X C B T See It!

20. Supplementary Angles Any two angles whose measures sum to 180. If mABC + m SXT = 180, then  ABC and  SXT are supplementary. S A  ABC is the supplement of  SXT  SXT is the supplement of  ABC X C T B See It!

21. Theorem If two angles are supplementary to congruent angles (the same angle) then they are congruent. If 1 suppl  2 and  2 suppl  3, then  1   3. 1 2 3

22. Theorem If two angles are complimentary to congruent angles (or to the same angle) then they are congruent. If 1 compl  2 and  2 compl  3, then  1   3. 1 2 3

23. Theorem Vertical angles are congruent (The definition of Vert. angles does not tell us anything about congruency… this theorem proves that they are.) 1 4 2 3

24. Perpendicular Lines () Two lines that intersect to form right angles. If l  m, then angles are right. l m See It!

25. Theorem If two lines are perpendicular, then they form congruent, adjacent angles. l If l  m, then 1  2. 2 1 m

26. Theorem If two lines intersect to form congruent, adjacent angles, then the lines are perpendicular. l If 1  2, then l  m. 2 1 m

27. Ch. 3

28. Parallel Lines ( or ) The way that we mark that two lines are parallel is by putting arrows on the lines. m || n m n

29. q p Skew Lines ( no symbol  ) Non-coplanar, non-intersecting lines. What is the difference between the definition of parallel and skew lines?

30. P Q Parallel Planes Planes that do not intersect. Can a plane and a line be parallel?

31. If two parallel lines are cut by a transversal, then corresponding angles are congruent. t r 1 2 4 3 5 6 s 7 8 Postulate Can you name the corresponding angles?

32. If two parallel lines are cut by a transversal, then alternate interior angles are congruent. t r 1 2 4 3 5 6 s 7 8 Theorem

33. If two parallel lines are cut by a transversal, then same side interior angles are supplementary. t r 1 2 4 3 5 6 s 7 8 Theorem

34. Show that corresponding angles are congruent Show that alternate interior angles are congruent Show that same side interior angles are supplementary In a plane, show that two lines are perpendicular to the same line Show that two lines are parallel to a third line Ways to Prove Lines are Parallel (pg. 85)

35. Types of Triangles(by sides) Isosceles 2 congruent sides Equilateral All sides congruent Scalene No congruent sides

36. Types of Triangles(by angles) Equiangular Acute 3 acute angels Right 1 right angle Obtuse 1 obtuse angle

37. Theorem The sum of the measures of the angles of a triangle is 180 B mA + mB + mC = 180 C A See It!

38. Corollary 3. In a triangle, there can be at most one _right____ or obtuse angle.

39. Theorem The measure of an exterior angle of a triangle equals the sum of the measures of the two remote interior angles m1 = m3 + m4 3 1 4 2 See It!

40. Regular Polygon • All angles congruent • All side congruent

41. Theorem (pg 102) The sum of the measures of the interior angles of a convex polygon with n sides is (n-2)180.

42. Theorem The sum of the measures of the exterior angles, one at each vertex, of a convex polygon is 360. 4 1 1 3 3 2 2 1 + 2 + 3 = 360 1 + 2 + 3 + 4 = 360

43. REGULAR POLYGONS • All the interior angles are congruent • All of the exterior angles are congruent (n-2)180 = the measure of each interior angle n 360 = the measure of each exterior angle n

44. Problems for Ch. 1 - 3 • 1 – 7 - 8 – 10 • 15 – 16 – 17 • 22 – 24 – 25 – 26 – 28 • 31 – 34 – 36

45. Ch. 4

46. Definition of Congruency Two polygons are congruent if corresponding vertices can be matched up so that: 1. All corresponding sides are congruent 2. All corresponding angles are congruent.

47. The order in which you name the triangles matters ! ABC DEF A E C B F D

48.  ABC   XYZ Based off this information with or without a diagram, we can conclude… Letters X and A, which appear first, name corresponding vertices and that  X   A. • The letters Y and B come next, so •  Y   B and • XY  AB

49. Five Ways to Prove  ’s All Triangles: ASA SSS SAS AAS Right Triangles Only: HL

50. Isosceles Triangle By definition, it is a triangle with two congruent sides called legs. X Vertex Angle Base Angles Z Y Legs Base