1. Unit 1: Basic Geometry
Wednesday, Aug 27th

2. Assignment Sheet Date Due Date Assignment Grade Done? 8/27
Points, Lines, and Planes Chart
8/28
Points, Lines, and Planes Wkst
_____/5pts
8/29
Points, Lines & Planes HW
9/12
Math Career Project
____/35pts

3. Warm Up & Journal: Aug 27th
Journal Prompt
5𝑥−11=19
6𝑥+18=54
−18+5𝑥=22
How do you plan to be successful in geometry this semester.
2-3 Sentences
Warm Up & Journal: Aug 27th

4. 1. Solving for x
5𝑥−11=19
+11
+11
5𝑥=30 5 5
𝑥=6

5. 2. Solving for x
6𝑥+18=54
−18
−18
6𝑥=36 6 6
𝑥=6

6. 3. Solving for x
−18+5𝑥=22
+18
+18
5𝑥=40 5 5
𝑥=8

7. Vocab Clear off your desk
Have out something to write with and your vocab chart

8. Point Picture: How is it drawn: dot Named By: letter
Facts: No Dimensional
Symbols:

9. Line Picture: How is it drawn: 2 Arrows and 2 Points
Named By: 2 Points or Cursive Letter
Facts: 1 dimensional, Straight, Infinite
Symbols:

10. Segment Picture: How is it drawn: 2 Endpoints Named By: 2 Endpoints
Facts: 1 Dimensional, Start and Stop, Distance
Symbols:

11. Ray Picture: How is it drawn: 1 Endpoint & 1 Arrow
Named By: Endpoint FIRST!!
Facts: 1 Dimensional, Extends in 1 Direction
Symbols:

12. Angle Picture: How is it drawn: 2 rays or intersecting lines
Named By: Vertex or 3 points
Facts: Obtuse, Acute, Straight, Right
Symbols:

13. Plane Picture: How is it drawn: 2 Angles
Named By: 4 Points or Bold Capital Letter
Facts: 2 Dimensional
Symbols: Plane S or Plane ABCD

14. Classwork

15. Homework
Due 8/29

16. Unit 1: Basic Geometry
Friday, Aug 29th

17. Assignment Sheet Date Due Date Assignment Grade Done? 8/27
Points, Lines, and Planes Chart
8/28
Points, Lines, and Planes Wkst
_____/5pts
8/29
Points, Lines & Planes HW
9/12
Math Career Project
____/35pts
Distance Formula Notes
9/2
Distance Formula WKST
____/10pts
**Have your HW out on your desk

18. Warm Up & Journal: Aug 29th
Journal Prompt
5𝑥−11=19
6𝑥+18=54
−18+5𝑥=22
Write 2-3 sentences.
Prompt:
Which career did you choose and why?
Warm Up & Journal: Aug 29th

19. Unit 1: Review Vocab
Vocabulary Quiz Monday

20. Definitions Collinear: On the same line. Coplanar: On the same plane.
Points A, B and C are collinear.
Collinear: On the same line. C B A
Coplanar: On the same plane. B A
Points A and B are coplanar
on plane R. R

21. B C D A H F E G A rectangular solid is made up of six planes.
Points A, D, E, and G are coplanar.
Points B, C, F, and H are coplanar.
Points A, B, C, and D are coplanar.
Points E, F, G, and H are coplanar.
Can you name more coplanar points?

22. Definitions
Line Segment: Made of two endpoints and all the collinear points between the endpoints. A B
Name a line segment using the letters of the endpoints.
𝑨𝑩 or 𝑩𝑨
What’s the difference between naming a line and naming a line segment?

23. Definitions
Ray: Has an initial point and extends forever in one direction. A
Name a ray by using the letter of the initial point and then the letter of another point on the ray. B 𝑨𝑩

24. What’s this?
It’s a line segment! A B
How do we name it?
𝑨𝑩 or 𝑩𝑨

25. What’s this?
It’s a line! B
How do we name it? A
𝑨𝑩 or 𝑩𝑨

26. What’s this?
It’s a ray! B A
How do we name it? 𝑨𝑩

27. The Distance Formula 𝑨𝑩= 𝒙 𝟐 − 𝒙 𝟏 + 𝒚 𝟐 − 𝒚 𝟏
The Distance Formula: A (x1 , y1) and B (x2 , y2) are points on the coordinate plane.
To find the distance between them, we would use this formula:
𝑨𝑩= 𝒙 𝟐 − 𝒙 𝟏 + 𝒚 𝟐 − 𝒚 𝟏 𝟐 𝟐
Steps to solve:
Identify & Label A (x1 , y1) and B (x2 , y2)
Plug in the numbers
Solve

28. Guide to Solving:

29. Example: What is the distance between points A and B?
𝑨𝑩= 𝒙 𝟐 − 𝒙 𝟏 + 𝒚 𝟐 − 𝒚 𝟏 𝟐 𝟐 B
Coordinates for point A?
Coordinates for point B?
A: −𝟔, 𝟕
B: 𝟐, 𝟑
𝒙 𝟏
𝒚 𝟏
𝒙 𝟐
𝒚 𝟐
𝑨𝑩= 𝟐 𝟐 (𝟐
−−𝟔) +
−𝟕) (𝟑
𝑨𝑩= 𝟖𝟎
𝑨𝑩= 𝟖 + −𝟒 𝟐 𝟐
𝑨𝑩=𝟖.𝟗 𝒖𝒏𝒊𝒕𝒔
𝑨𝑩= 𝟔𝟒+𝟏𝟔

30. What is the distance between points A and B?
𝒙 𝟏
𝒚 𝟏
𝒙 𝟐
𝒚 𝟐 B
𝑨𝑩= 𝒙 𝟐 − 𝒙 𝟏 + 𝒚 𝟐 − 𝒚 𝟏 𝟐 𝟐
𝑨𝑩= (𝟔
−−𝟓) + 𝟐
−𝟒)
(−𝟐
𝑨𝑩= 𝟏𝟓𝟕 𝟐
𝑨𝑩= 𝟏𝟏 𝟐 + −𝟔 𝟐
𝑨𝑩=𝟏𝟐.𝟓 𝒖𝒏𝒊𝒕𝒔
𝑨𝑩= 𝟏𝟐𝟏+𝟑𝟔

31. What is the distance between points A and B?
𝑨𝑩= 𝒙 𝟐 − 𝒙 𝟏 + 𝒚 𝟐 − 𝒚 𝟏 𝟐 𝟐 A
𝑨𝑩= (𝟔
−−𝟔) + 𝟐
(−𝟐
−−𝟓)
𝑨𝑩= 𝟏𝟓𝟑 𝟐
𝑨𝑩= 𝟏𝟐 𝟐 + 𝟑 𝟐
𝑨𝑩=𝟏𝟐.𝟒 𝒖𝒏𝒊𝒕𝒔
𝑨𝑩= 𝟏𝟒𝟒+𝟗

32. Unit 1: Basic Geometry
Wednesday, Sept 3rd

33. Binder Check!! Is your binder in this order? Syllabus About Me Rubric
Unit 1 Title Page
Assignment Sheet
Warm Up/Journal
Vocabulary

34. Assignment Sheet Date Due Date Assignment Grade Done? 8/27
Points, Lines, and Planes Chart
8/28
Points, Lines, and Planes Wkst
_____/5pts
8/29
Points, Lines & Planes HW
9/12
Math Career Project
____/35pts
Distance Formula Notes
9/2
Distance Formula WKST
____/10pts
Unit 1: Quiz #1
____/15pts
9/3
Segment Addition Foldable
9/4
Segment Addition Wkst
___/10pts
**Have your HW out on your desk

35. Foldable

36. Segment Addition Postulate: If L is between K and M, then 𝑳𝑲 + 𝑲𝑴 = 𝑳𝑴 .

39. Example 𝟓𝒙+𝟒 GH: 𝟑𝒙−𝟕 𝟑𝒙−𝟕 HI: 𝟓𝒙+𝟒 G H I GI: 𝟐𝟏 𝟑𝒙−𝟕 + 𝟓𝒙+𝟒 =𝟐𝟏 𝟐𝟏
Suppose H is between G and I. Using the segment addition postulate find the length of each segment.
𝟓𝒙+𝟒
GH: 𝟑𝒙−𝟕
𝟑𝒙−𝟕
HI: 𝟓𝒙+𝟒 G H I
GI: 𝟐𝟏
𝟑𝒙−𝟕 + 𝟓𝒙+𝟒 =𝟐𝟏 𝟐𝟏
𝟖𝒙−𝟑=𝟐𝟏 +𝟑 +𝟑
GH: 𝟑 𝟑 −𝟕
HI: 𝟓 𝟑 +𝟒
𝟖𝒙=𝟐𝟒 𝟖 𝟖
GH: 𝟗−𝟕
HI: 𝟏𝟓+𝟒
𝒙=𝟑
GH: 𝟐
HI: 𝟏𝟗

40. Example 𝟔𝒙−𝟓 AB: 𝟐𝒙+𝟑 𝟐𝒙+𝟑 BC: 𝟔𝒙−𝟓 A B C AC: 𝟑𝟎 𝟐𝒙+𝟑 + 𝟔𝒙−𝟓 =𝟑𝟎 𝟑𝟎
Suppose B is between A and C. Using the segment addition postulate find the length of each segment.
𝟔𝒙−𝟓
AB: 𝟐𝒙+𝟑
𝟐𝒙+𝟑
BC: 𝟔𝒙−𝟓 A B C
AC: 𝟑𝟎
𝟐𝒙+𝟑 + 𝟔𝒙−𝟓 =𝟑𝟎 𝟑𝟎
𝟖𝒙−𝟐=𝟑𝟎 +𝟐 +𝟐
AB: 𝟐 𝟒 +𝟑
BC: 𝟔 𝟒 −𝟓
𝟖𝒙=𝟑𝟐 𝟖 𝟖
AB: 𝟖+𝟑
BC: 𝟐𝟒−𝟓
𝒙=𝟒
AB: 𝟏𝟏
BC: 𝟏𝟗

41. Homework
Segment Addition Postulate Worksheet

42. Unit 1: Basic Geometry
Thursday, Sept 4th

43. Assignment Sheet Date Due Date Assignment Grade √ 8/27 9/12
Math Career Project
____/35pts
8/29
Distance Formula Notes
9/2
Distance Formula WKST
____/10pts
Unit 1: Quiz #1
____/15pts
9/3
Segment Addition Foldable
9/4
Segment Addition Wkst
___/10pts
Midsegment Notes
9/5
Midsegment & Distance WKST
**Have your HW out on your desk

44. Warm Up & Journal: Sept. 4th
Journal Prompt
𝐹𝑖𝑛𝑑 𝑡ℎ𝑒 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒.
A(-4, 10) B(2, -3)
2. Solve for AB & BC.
B is between A & C.
AC = 22
BC = x+14
AB = x+10.
Compare & Contrast a line, segment, and ray.
2-3 Sentences
Warm Up & Journal: Sept. 4th

45. Homework Check

46. Definition
Midpoint: point on a line segment that bisects it (divides it into two equal parts). K T M
𝑻𝑴 ≅ 𝑴𝑲

47. Example M is the midpoint of 𝑻𝑲 . Find the value of 𝒙. 𝟏𝟑𝒙−𝟑 𝟏𝟓𝒙−𝟗 K T
𝟏𝟑𝒙−𝟑=𝟏𝟓𝒙−𝟗
−𝟏𝟑𝒙
−𝟏𝟑𝒙
−𝟑=𝟐𝒙−𝟗 +𝟗 +𝟗
𝟔=𝟐𝒙 𝟐 𝟐
𝟑=𝒙

48. What is the midpoint of 𝑨𝑩?
Coordinate Midpoint Theory: If (x1 , y1) and (x2 , y2) are the coordinates of the endpoints of a segment, then the coordinates of the midpoint are
What is the midpoint of 𝑨𝑩?
A: (2, 2) B: (6, -8) A C C: B

49. Example
A: (-2, 3) B: (-4, -5)
What is the midpoint of AB? A C B C:

50. Example
What do you do when you know one endpoint, the midpoint, and you are looking for the other endpoint?
A: (5, 5) M: (3, -1) A
What is the other endpoint B of this segment? M
𝒙 𝟏 + 𝒙 𝟐 𝟐 = 𝒎 𝒙 B
𝒙 𝟏 + 𝒙 𝟐 =𝟐 𝒎 𝒙
𝒙 𝟐 =𝟐 𝒎 𝒙 − 𝒙 𝟏
𝒚 𝟐 =𝟐 𝒎 𝒚 − 𝒚 𝟏

51. Example
A: (5, 5) M: (3, -1) A
What is the other endpoint B of this segment? M 𝟐 𝟐 B 𝟐 𝟐
B: (1
, -7)

52. Another Cheesy Way 𝑨:(𝟓, 𝟓) 𝑴:(𝟑, −𝟏) 𝑴:(𝟑, −𝟏) 𝑩:(𝟏, −𝟕)
Here’s what you should do when you know one endpoint, the midpoint, and you are looking for the other endpoint!
𝑨:(𝟓, 𝟓)
𝑴:(𝟑, −𝟏) −𝟐 −𝟔
𝑴:(𝟑, −𝟏) −𝟐 −𝟔
𝑩:(𝟏, −𝟕)
Arrange the endpoint and midpoint vertically.
Find the difference and apply it again.
Much easier this way isn’t it?

54. Vocab

55. Vocab

56. Vocab

57. Vocab

58. Vocabulary Matching

60. Unit 1: Basic Geometry
Monday, Sept 8th

61. Assignment Sheet Date Due Date Assignment Grade √ 8/27 9/12
Math Career Project
____/35pts
8/29
Distance Formula Notes
9/2
Distance Formula WKST
____/10pts
Unit 1: Quiz #1
____/15pts
9/3
Segment Addition Foldable
9/4
Segment Addition Wkst
___/10pts
Midpoint Notes
9/5
Midpoint & Distance WKST
9/8
Angle Notes
**Have your HW out on your desk

62. ≅ Definitions You read this symbol by saying “is congruent to”.
Side AB is congruent to side AC
𝑨𝑩 ≅ 𝑨𝑪
3.1 cm
3.1 cm B C

63. Definitions Angle: Formed when two rays share a common endpoint. A B C
You can name this angle ABC or CBA. You can use the angle symbol ∠ to say ∠ 𝑨𝑩𝑪 or ∠𝐂𝐁𝐀
If there is only one angle with vertex B, you can name this angle ∠𝑩

64. Naming Angles
If a vertex has more than one angle, you must use the endpoints and vertex to name the angle.
What is the name of the red angle? A
∠𝑨𝑩𝑫 or ∠𝑫𝑩𝑨 D
What is the name of the green angle?
∠𝑨𝑩𝑪 or ∠𝑪𝑩𝑨 B C
What is the name of the purple angle?
∠𝑫𝑩𝑪 or ∠𝑪𝑩𝑫

65. Definitions
Vertex: Common endpoint of the two rays that make an angle. A
Point B is the vertex of ∠𝑨𝑩𝑪 B C
Sides: The two rays that make up the angle. A
side
𝑩𝑨 and 𝑩𝑪 are sometimes called sides. B C
side

66. Definitions
Measure of an angle: Smallest amount of rotation about the vertex from one ray to the other. Use a curved line to indicate the angle. A
𝟐𝟒° B C
Degrees: The unit of measure for angles. Indicates the amount of rotation.
∠𝑨𝑩𝑪=𝟐𝟒°

67. Definitions
Congruent Angles: Angles that have the same degree measure. Used a curved line above an equal sign to indicate congruence. A X ≅ B Y C Z
∠𝑨𝑩𝑪≅∠𝑿𝒀𝒁
Said: “Angle ABC is congruent to angle XYZ.”

68. Practice Name all the angles in this figure. P ∠𝑷𝑿𝑮 ∠𝑮𝑿𝑴 X ∠𝑷𝑿𝑴 ∠𝑿𝑴𝑮
∠𝑿𝑮𝑨
∠𝑿𝑮𝑴
∠𝑴𝑮𝑨 M G A

69. Definitions
Adjacent Angles: Angles that have a common ray or side and a common vertex, but points inside either one of the angles are not inside the other. A B C Z
∠𝑨𝑩𝑪
is adjacent to
∠𝑪𝑩𝒁

70. Angle Addition PostulateR
Angle Addition Postulate: ∠𝑹𝑪𝑴+
∠𝑴𝑪𝑷
= ∠𝑹𝑪𝑷. C M P

71. Definitions
Angle Bisector: Contains the vertex and divides an angle into two equal halves. Splits the angle in half. X B Y Z
𝒀𝑩 bisects ∠𝑿𝒀𝒁

72. Example Angle Bisector X B Y Z 𝒀𝑩 bisects ∠𝑿𝒀𝒁 ∠𝑿𝒀𝒁=𝟗𝟎°
What is the degree measure of ∠𝑿𝒀𝑩 ?
=𝟒𝟓°
∠𝑩𝒀𝒁 ?
=𝟒𝟓°

73. Types of Angles Right Angle: Angle that measures exactly 𝟗𝟎°. A B C
Acute Angle: Angle that measures less than 𝟗𝟎°. A 50 B C

74. Types of Angles
Obtuse: Angle that measures more than 𝟗𝟎° A
𝟏𝟐𝟎° B C

75. 𝐖𝐫𝐢𝐭𝐞 𝐭𝐰𝐨 𝐧𝐚𝐦𝐞𝐬 𝐟𝐨𝐫 𝐞𝐚𝐜𝐡 𝐡𝐢𝐠𝐡𝐥𝐢𝐠𝐡𝐭𝐞𝐝 𝐚𝐧𝐠𝐥𝐞.
𝐄𝐬𝐭𝐢𝐦𝐚𝐭𝐞 𝐰𝐡𝐞𝐭𝐡𝐞𝐫 𝐞𝐚𝐜𝐡 𝐚𝐧𝐠𝐥𝐞 𝐢𝐬 𝐚𝐜𝐮𝐭𝐞, 𝐫𝐢𝐠𝐡𝐭,
𝐨𝐛𝐭𝐮𝐬𝐞 𝐨𝐫 𝐬𝐭𝐫𝐚𝐢𝐠𝐡𝐭. F A D E B C G

76. Types of Angles
Straight: The angle measure for a straight line is 𝟏𝟖𝟎°
𝟏𝟖𝟎° A B C

77. Types of Angles
Vertical Angles: congruent angles formed by intersecting lines or line segments.

78. Types of Angles What are the vertical angles in this figure? ∠𝑨𝑬𝑩≅∠𝑪𝑬𝑫B A
∠𝑨𝑬𝑩≅∠𝑪𝑬𝑫 E
∠𝑨𝑬𝑪≅∠𝑩𝑬𝑫 C D

79. Example Find the value of the variable. 𝟐𝟓𝒙−𝟖=𝟗𝟐 B +𝟖 +𝟖 A 𝟐𝟓𝒙=𝟏𝟎𝟎 𝟐𝟓
𝟗𝟐° E
𝒙=𝟒 C D

80. Example Find the value of the variable. 𝟑𝟓𝒙−𝟐𝟓=𝟑𝟐𝒙−𝟏𝟎 −𝟑𝟐𝒙 −𝟑𝟐𝒙 B
𝟑𝒙−𝟐𝟓=−𝟏𝟎 A
+𝟐𝟓
+𝟐𝟓
𝟑𝒙=𝟏𝟓 𝟑 𝟑
𝟑𝟓𝒙−𝟐𝟓 E
𝟑𝟐𝒙−𝟏𝟎
𝒙=𝟓 C D

81. Example Find the value of the variable. B A 𝟑𝒙+𝟔 +(𝟏𝟎𝒙−𝟖)=𝟏𝟖𝟎
𝟏𝟑𝒙−𝟐=𝟏𝟖𝟎
(𝟑𝒙+𝟔)° +𝟐 +𝟐
𝟏𝟑𝒙=𝟏𝟖𝟐 𝟏𝟑 𝟏𝟑
𝒙=𝟏𝟒
(𝟏𝟎𝒙−𝟖)° E D C

82. Example Find the value of the variables. 𝟐𝟎𝒙+𝟏𝟐 +(𝟏𝟓𝒙−𝟕)=𝟏𝟖𝟎 A
𝟑𝟓𝒙+𝟓=𝟏𝟖𝟎 −𝟓 −𝟓 D
𝟑𝟓𝒙=𝟏𝟕𝟓
(𝟐𝟎𝒙+𝟏𝟐)°
𝟐𝟎 𝟓 +𝟏𝟐° 𝟑𝟓 𝟑𝟓 𝒚
𝒙=𝟓 E
(𝟏𝟓𝒙−𝟕)°
𝟐𝟎 𝟓 +𝟏𝟐° B
𝟏𝟏𝟐°
𝟏𝟖𝟎°−𝟏𝟏𝟐°=𝒚 C
𝒚=𝟔𝟖

83. Types of Angles A D B E S P Q T R U
Complementary Angles: two or more angles that add up to 𝟗𝟎°.
∠𝑨𝑩𝑫 and ∠𝑫𝑩𝑬 are adjacent complementary angles A D
∠𝑨𝑩𝑫 +∠𝑫𝑩𝑬=𝟗𝟎° B E S
∠𝑷𝑸𝑹 𝒂𝒏𝒅 ∠𝑺𝑻𝑼 P
are nonadjacent complementary angles
𝟑𝟓°
𝟓𝟓° Q T R U
∠𝑷𝑸𝑹+∠𝑺𝑻𝑼=𝟗𝟎°

84. Supplementary Angles: two angles that add up to 𝟏𝟖𝟎°. D
∠𝑫𝑩𝑬 + ∠𝑫𝑩𝑪=𝟏𝟖𝟎° E B C
∠𝑫𝑩𝑬 𝒂𝒏𝒅 ∠𝑫𝑩𝑪 are adjacent supplementary angles
They would also be called a linear pair because they form a straight line
∠𝑨𝑹𝑻 𝒂𝒏𝒅 ∠𝑩𝑳𝑴 are nonadjacent
supplementary angles
∠𝑨𝑹𝑻+∠𝑩𝑳𝑴=𝟏𝟖𝟎° B A
𝟏𝟐𝟓°
𝟓𝟓° L R T M

85. Example
Use the marks on the diagram to name the congruent segments and congruent angles. A
𝑨𝑩 ≅ 𝑩𝑪
∠𝑫𝑨𝑩≅ ∠𝑫𝑪𝑩
𝑨𝑫 ≅ 𝑪𝑫
∠𝑨𝑫𝑩≅ ∠𝑪𝑫𝑩 B D C

86. Example D A B C 𝑩𝑫 bisects ∠𝑨𝑩𝑪. Find the value of x. (𝟒𝒙+𝟏𝟎)°
(𝟏𝟎𝒙−𝟔𝟖)° B C
𝟒𝒙+𝟏𝟎=𝟏𝟎𝒙−𝟔𝟖
What if you were asked the degree measure of ∠𝑨𝑩𝑫?
−𝟒𝒙
−𝟒𝒙
𝟏𝟎=𝟔𝒙−𝟔𝟖
𝟒 𝟏𝟑 +𝟏𝟎
+𝟔𝟖
+𝟔𝟖
𝟓𝟐+𝟏𝟎
𝟕𝟖=𝟔𝒙
𝟔𝟐° 𝟔 𝟔
𝟏𝟑=𝒙

87. Example D A B C 𝑩𝑫 bisects ∠𝑨𝑩𝑪. Find the value of x. Find ∠𝑨𝑩𝑫
(𝟔𝒙−𝟏𝟗)°
(𝟐𝒙 +𝟏𝟕)° B C
𝟔𝒙−𝟏𝟗=𝟐𝒙+𝟏𝟕
−𝟐𝒙
−𝟐𝒙
∠𝑨𝑩𝑫=𝟔𝒙−𝟏𝟗
𝟒𝒙−𝟏𝟗=𝟏𝟕
𝟔 𝟗 −𝟏𝟗
+𝟏𝟗
+𝟏𝟗
𝟓𝟒−𝟏𝟗
𝟒𝒙=𝟑𝟔
𝟑𝟓° 𝟒 𝟒
𝒙=𝟗