Angle Relationships

1. Angle Relationships Page 76

2. Complimentary Angles • Two angles whose measures add up to ______ Example: ABC and CBD are complimentary angles

3. Supplementary Angles • Two angles whose measures add up to ______ Example: EFG and GFH are supplementary angles

4. Congruent Angles • When two or more angles have the same measure, they are ___________________ -Equality shown with matching markings

5. Notice • Two angles _________need to share a vertex and a common side to be complimentary, supplementary, or congruent

7. Naming Parts of Shapes Page 81

8. A Point • Named by using a single ____________ letter Example: Points A, B, and C

9. Prime Notation • When a shape is transformed, the new shape is named using_________________________ Example: The new point A is labeled as A’ (read as “A ↓ prime”) ↓

10. Line Segment • Named by naming its ___________ and placing a __________above them. Example: , , , , ,

11. Line • Lines extend ____________ in either direction • Named by naming two points on a line and placing a bar with arrows above them Example: , , , , ,

12. Angle • Named by using an __________ symbol in front of the name of the angle’s vertex • Example: A is the angle measuring 80°

13. Angle • Sometimes a single letter isn’t enough. • When more than one angle share a vertex, The angle is named with _______ letters (using the vertex as the ____________ letter) Example: HGI or IGH are referring to the angle measuring 10°

14. Angle’s Measure • To refer to an angle’s measure, place m in ________ of the angle’s name Example: m HGI=10° means “the measure of HGI is 10°”

15. Transversal • A ________ that crosses two or more lines • Example: is a transversal

16. Vertical Angles • Two _____________angles formed by two intercepting lines • Always have _____________ value (congruent) • Example: c and d are a pair of vertical angles

17. Corresponding Angles • Lie at the _________ position but different points of intersection of the transversal • Congruent IF the lines intersecting the transversal are __________________ • Example: d and m are corresponding angles (both to the right of transversal and above the intersecting line)

19. Systems of Linear Equations Page 87

20. Systems of Linear Equations • Set of two or more _____________equations that are given together • Example: y = 2x y = -3x + 5

21. Point of Intersection • The point that makes ________ equations true • Where the lines ________________ if graphed • Example: Point of intersection: (1, 2)

22. Coincide • The graphs of the two lines lie on _________ of each other • __________________number of intersections • Example:

23. NO Points of Intersection • Then the lines are ____________________ • They will ________________ intersect • Example:

24. Equal Values Method • When the two equations have the ________ variable already by itself (ex: y-form) • Set them ______________ to each other • Solve for one variable • Plug in the value for the solved variable and ____________ to find the value of the other variable.

25. Ex: y = 2x – 3 and y = -4x +3 If y = a and y = b, then a = b 2x – 3 = -4x + 3 Solve for y

26. Substitution Method

27. Ex: 2x + 5y = 31 and 3x + y = 1

28. Elimination Method • Step 1—Arrange the two equations in columns (so each variable and constant are lined up) • Step 2—Multiply one equation, if necessary, so that you have opposite coefficients for one variable (ex. 2x and -2x) • Step 3—add the equations from step 2 (remember this is called elimination method because you want to get rid of one of the variables during this step)

29. Elimination (continued)

30. Ex: x + 5y = 8 x – 5y = 4

31. More Angle Pair Relationships Page 91

32. Alternate Interior Angles • Angles that are ________ the pair of lines and on opposite side of the transversal • Congruent IF lines intersecting transversal are _________________ • Example: ∠f and ∠m are alternate interior angles

33. Same-Side Interior Angles • _________ side of transversal and in between the pair of intersecting lines • Supplementary IF intersecting lines are _____________ • Example: ∠g and ∠m are same-side interior angles

37. Proof By Contradiction Page 96

38. Definition • Prove a claim by thinking about what the consequences would be if it were _____________. If the claim being false would lead to an impossibility, that shows that the claim must be ______________.

39. Set-Up Suppose… Then… But this is impossible, so…

40. Example Prove that the lines and are parallel by proof by contradiction.

41. Suppose and intersect at some point E. Then the angles in AEC add up to more than But this is impossible, so and must be parallel.

43. Definition • The measures of all angles in a triangle add up to _____________

44. Example m A + m B + m C =

45. Tiling Example • The three angles of a triangle form a straight edge, therefore the sum of the angles of a triangle must be _________

47. Multiplying Binomials Page 104

48. Use each factor of the product as a dimension of a rectangle and find its area • Example (2x + 5)(3x - 1) (2x + 5)(3x - 1) =

49. Conditional Statement Page 108

50. Written in the form: “If …, then…” • Examples: 1) If a shape is a rhombus, then it has four sides of equal length. 2) ____ it is February 14th, ___________it is Valentine’s Day.