Unit 1: Basic Geometry Wednesday, Aug 27th

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

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

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

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

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

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

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

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

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

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

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

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

Classwork

Homework Due 8/29

Unit 1: Basic Geometry Friday, Aug 29th

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

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

Unit 1: Review Vocab Vocabulary Quiz Monday

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

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?

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?

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

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

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

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

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

Guide to Solving:

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

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

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

Unit 1: Basic Geometry Wednesday, Sept 3rd

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

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

Foldable

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

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

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

Homework Segment Addition Postulate Worksheet

Unit 1: Basic Geometry Thursday, Sept 4th

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

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

Homework Check

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

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

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

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

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

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)

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?

Vocab

Vocab

Vocab

Vocab

Vocabulary Matching

Unit 1: Basic Geometry Monday, Sept 8th

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

≅ 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

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

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

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

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°

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.”

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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°

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

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

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

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