1. Solve the equations 8x - 4 = 3x - 39 5 (x - 9) = 2x + 15
Tuesday 04/23 Warm Up
Solve the equations
8x - 4 = 3x - 39
5 (x - 9) = 2x + 15
4x - 10 = x + 3x - 2x

2. What is a “systems” of equations?
Two (or more) linear equations
What is the solution to a system of equations?
The ordered pair (x, y) at which the lines intersect

3. What is it? Steps to Solve
Substitution Method
What is it?
A method for solving systems of equations by substituting equations within each other
Steps to Solve
Step 1 : Solve one equation for x or y
Step 3: Substitute your answer into the revised equation from Step 1 and solve for the other variable
Step 2: Substitute this expression into the other equation and solve for the variable

4. Example 1:
y = 6x
2x + 3y = -20
2x - 3y = -11
2x + y = 9
Example 2:

5. You Try!
y = x + 9
3x + 8y = -5
2x + y = -2
5x + 3y = -8
You Try!

6. What is it? Steps to Solve Elimination Method
A method of solving systems by adding or subtracting equations to eliminate a variable
Steps to Solve
Step 1: Make sure equations are lined up!
Step 3: Solve the equation for the remaining variable.
Step 2: Add or subtract equations to eliminate the variable with common coefficients
Step 4: Substitute your answer into either original equation and solve for the other variable.

7. Example 1:
x + 4y = 13
x - y = 3
x + 3y = 6
2x - 7y = -1
Example 2:

8. You Try!
3x - 10y = 14
3x - 9y = 15
9x + 3y = 12
2x + y = 5
You Try!

9. Wednesday 04/24 Warm Up
System A: Choose your method Substitution or Elimination
8x + 5y = -13
3x + 4y = 10
System B: Choose your method Substitution or Elimination
4x - 3y = 18
2x + y = 4

10. Lines that never touch and are always the same distance apart
Vocabulary
Parallel Lines
Lines that never touch and are always the same distance apart

11. A line that intersects more than one line
Vocabulary
Transversal
A line that intersects more than one line

12. Angles whose sum is 180 degrees
Vocabulary
Supplementary Angles
Angles whose sum is 180 degrees

13. Angles whose sum is 90 degrees
Vocabulary
Complementary Angles
Angles whose sum is 90 degrees

14. Vocabulary
Congruent
Same size and shape. Fancy word for equal (Equal angles, side lengths, etc)

15. Parallel Lines and Transversals
Name the parallel lines
Name the transversal

16. Vertical Angles are congruent Vertical Angles
Name and highlight the pairs vertical angles
<1 and <4
<2 and <3
<5 and <8
<6 and <7

17. Corresponding angles are congruent
Congruent Angles
Corresponding angles are
congruent
Name and highlight the corresponding angles.
<1 and <5
<2 and <6
<3 and <7
<4 and <8
Hint: Which ones match up in the same location?

18. Alternate Interior Angles
Alternate Interior are
congruent
Name and highlight the alternate interior angles
<3 and <6
<4 and <5
Hint: Alternate means opposite side of the transversal. Interior means inside of the parallel lines.

19. Alternate Exterior Angles
Alternate exterior are
congruent
Name and highlight the alternate exterior angles
<1 and <8
<2 and <7
Hint: alternate means opposite sides of the transversal. Exterior means outside,

20. Same side Interior Angles
Same side interior angles are
supplementary
Name and highlight the same side interior angles
<3 and <5
<4 and <6
Hint: Same side means on the same side of the transversal. Interior means inside.

21. Same side Exterior Angles
Same side exterior angles are
supplementary
Name and highlight the alternate exterior angles
<1 and <7
<2 and <8
Hint: Same side of transversal. Exterior means outside.

22. Given m∠1 is 120 degrees. Find the measure of all other angles.
Example
Given m∠1 is 120 degrees. Find the measure of all other angles.

23. Get out your assignment sheet to be signed!
Thursday 04/25 Warm Up
Get out your assignment sheet to be signed!
Given the following, solve for x.

24. Dilations Discovery Activity

25. Dilations
Dilation is a transformation in which a polygon is enlarged or reduced by a given factor around a given center point.

26. k represents the scale factor and how the polygon will grow.
Dilations
k represents the scale factor and how the polygon will grow.
If k > 1, the polygon will grow
If 0 < k < 1, the polygon will shrink
If k = 1, the polygon will stay the same

27. To find the dilated coordinates...
Multiply the x and y value by k!
Example: Dilate the figure by a scale factor of k = 2. Will it grow, shrink or stay the same?

28. Simplify the following using exponent properties
Friday 04/26 Warm Up
Simplify the following using exponent properties

29. Solve the following proportions
Monday 04/29 Warm Up
Solve the following proportions

30. Motivational Monday

31. Similar Triangle Doodle Notes

32. Open your booklets to page 20 Complete #1-6
Tuesday 04/30 Warm Up
Open your booklets to page 20 Complete #1-6

33. Check Worksheet Homework

34. Finish Similar Triangle Doodle Notes

35. Triangle Midsegment
A midsegment of a triangle is a segment that connects the midpoints of two sides of a triangle.
What is a midpoint?

36. Triangle Midsegment
In a triangle, the segment joining the midpoints of any two sides of a triangles will be parallel to the third side and half its length OR

37. Example
Answer:
CD = 8

38. Example
Answer:
AC = 8

39. You Try!
Answer:
KI = 10

40. You Try!
Answer:
KJ = 9

41. Example
Answer:
X = -9

42. Example
Answer:
X = 5

43. You Try!
Answer:
X = 12

44. You Try!
Answer:
X = 12

45. Triangle Midsegment Theorem Folding Activity
Cut out a triangle (any size!) and label the vertices (corners) as A, B, and C
Fold A to C (don’t crease!) and pinch/label the midpoint as L.
Fold B to C (don’t crease!) and pinch/label the midpoint as N.
Fold C to the bottom of the triangle and draw in the line to connect L and N.
Fold in B to C and A to C to create a rectangle.
How does LN compare to AB?

46. Homework: pg. 21 #

47. Open your booklets to page 31 Complete #1 - 6
Thursday 05/02 Warm Up
We are in May!!!!!!!!
Open your booklets to page 31 Complete #1 - 6

48. Check Homework: pg. 21 #

49. Isosceles Triangle Theorem Guided Notes

50. Homework: Worksheet

51. Open your booklets to page 33 Complete #10 - 14
Friday 05/03 Warm Up
Open your booklets to page 33 Complete #

52. Check Homework Worksheet

53. Complete page 10 in your workbook!
Monday 05/06 Warm Up
Complete page 10 in your workbook!

54. Motivational Monday

55. Used to find missing side of a right triangle hypotenuse
Pythagorean Theorem
Used to find missing side of a right triangle
hypotenuse c
For any right triangle:
a2 + b2 = c2 a
legs b

56. Examples

57. Trigonometry: The study of triangle measurement

58. Trigonometric Ratios
Sine: The ratio of the leg opposite the angle to the angle to the hypotenuse
Cosine: The ratio of the leg adjacent the angle to the angle to the hypotenuse
Tangent: The ratio of the leg opposite the angle to the leg adjacent to the angle

59. SOH - CAH - TOA SOH CAH TOA Some Old Hippie Caught Another Hippie
REMEMBER!!!
SOH CAH TOA
Some Old Hippie
Caught Another Hippie
Trippin On Asphalt
SOH - CAH - TOA
Sin = opp/hyp
Tan = opp/adj
Cos = adj/hyp

60. Give each trig ratio as a fraction in simplest form

61. Homework page 52-53

62. Tuesday 05/07 Warm Up

63. Check Homework page 53

64. Finding Side Lengths Using Trig
Note: Make sure your calculator is in degree mode

65. Your Turn!

66. Homework page

67. Wednesday 05/08 Warm Up

68. Check homework page 61

69. AGAIN! Make sure your calculator is in degree mode!
Inverse SOH CAH TOA
If you know the sin, cosine or tangent ratio of an angle, you can use the inverse of the ratio (sin-1, cos-1, tan-1) to find the measure of the angle.
AGAIN! Make sure your calculator is in degree mode!

70. Finding Angle Measures

71. Your Turn!

72. Homework page

73. Thursday 05/09 Warm Up

74. Check homework page

75. Applications Angle of Elevation
When looking UP to an object, the angle of elevation is formed by an observer’s line of sight and a horizontal line.
Angle of Depression
When looking DOWN to an object, the angle of depression is formed by an observer’s line of sight and a horizontal line.
The angle of depression is congruent to the angle of elevation because they are alternate interior angles.

76. Examples
Casey sights the top of an 84 ft tall lighthouse at and angle of elevation of 58°. If Casey is 6 feet tall, how far is he standing from the base of the lighthouse?
A lifeguard is sitting on a platform, looking down at a swimmer in the water. If the lifeguard’s line of sight is 8 ft above the ground and the angle of depression to the swimmer is 18°, how far away is the swimmer from the lifeguard?

77. Review

78. Friday 05/10 Warm Up

79. You Try!
The angle of elevation from a kicker’s foot on the football field to the top of the goal post bars is 17°. If he is standing 131 ft. from the base of the goal post, how tall is the goal post?
A pilot in a helicopter spots a landing pad below. If the angle of depression is 73° and the horizontal distance to the pad is ft., what is the altitude of the helicopter?

80. Review

81. SOH CAH TOA Task Cards

82. Monday 05/13 Warm Up
Elijah is looking up to the top of the Washington Monument. If the monument is 555 ft. tall and the angle of elevation from the point on the ground where Elijah is standing to the top is 74°, how far is he standing from the base of the monument?
The angle of depression from an airplane to the TOP of an air traffic control tower is 56°. If the tower is 320 feet tall and the airplane is flying at an altitude of 7,450 ft., how far away is the airplane from the control tower?

83. Motivational Monday

84. Triangle Guide Book

85. Study Guide!

86. Turn in:
Assignment Sheet
Workbook
Study Guide
TEST DAY!

87. Wednesday 05/15 Warm Up
Find the dilated coordinates with the given scale factor.
S(3, -5), T(0, -2), U(-3, -5), V(0, -8)
Scale factor = 4
S’:____ T’:____ U’:____ V’:____
F(-6, -5), G(3, -4), H(3, -7)
Scale factor = ⅛
F’:____ G’:____ H’:____