How are Vertical Angle created? Vertical Angles Date: 10.08.2018 1. Write down the Essential Question (EQ). 2. Work on the Warm up. Essential Question How are Vertical Angle created? Warm Up: Explain the two pictures 1. 2.

There is a line that is cut by another line. 𝐴° 𝐵°

Core Concept Two adjacent angles are a linear pair if their sides from a line.

There is a line that is cut by another line. 𝐴° 𝐵° 𝐵° 𝐴°

Core Concept Two angles are vertical angles if they are not adjacent and their sides are formed by two intersecting lines.

There is a line that is cut by another line. 120° 60° 60° 120°

Parallel Lines and Transversals Date: 10.09.2018 1. Write down the Essential Question (EQ). 2. Work on the Warm up. Essential Question How does the transversals line affect the angles on a parallel lines ? Warm Up: Explain the joke

There is a line that is cut by another line. 𝐴° 𝐵° 𝐵° 𝐴°

Now extend the red cut line. Its now cut through a parallel black line 𝐴° 𝐵° 𝐵° 𝐴°

𝐴° 𝐵° 𝐵° 𝐴° Vocabulary Symbols to show that the two lines are parallel The red line is called the transversal line. It is a line that cut/intersection two or more lines at different point

Watch the line slides 𝐴° 𝐵° 𝐵° 𝐴°

Watch the line slides back 𝐴° 𝐵° 𝐵° 𝐴°

𝐴° 𝐵° 𝐵° 𝐴°

𝐴° 𝐵° 𝐵° 𝐴° 𝐴° 𝐵° 𝐵° 𝐴° Core Concept “A” Because the lines are parallel, they shares the same identical angles. 𝐴° 𝐵° 𝐵° 𝐴°

𝐴° 𝐵° 𝐵° 𝐴° 𝐴° 𝐵° 𝐵° 𝐴°

𝐴° 𝐵° 𝐵° 𝐴° 𝐴° 𝐵° 𝐵° 𝐴° Core Concept “B” Because the inside angles have to be a linear pair.. 𝐴° 𝐵° 𝐵° 𝐴°

Replace the variable with numbers 1 𝐴° 𝐵° 2 𝐵° 3 4 𝐴° 5 𝐴° 𝐵° 6 𝐵° 7 8 𝐴°

1 2 3 4 5 6 7 8

1 2 3 4 5 6 7 8 Core Concept Two angles are corresponding angles when they have the same corresponding position. 5 6 7 8

1 2 3 4 5 6 7 8 Core Concept corresponding angles ∠1 ≅∠5 ∠2 ≅∠6 ∠3 ≅∠7 ∠4 ≅∠8 5 6 7 8

1 2 3 4 5 6 7 8

1 2 3 4 Two angles are alternate interior angles when they are on opposite side and lie inside the two parallel lines. 5 6 7 8

1 2 3 4 Alternate Interior Angles ∠3 ≅∠6 ∠4 ≅∠5 5 6 7 8

1 2 3 4 5 6 7 8

1 2 3 4 Two angles are alternate exterior angles when they are on opposite side and lie outside the two parallel lines. 5 6 7 8

1 2 3 4 Alternate exterior Angles ∠1 ≅∠8 ∠2 ≅∠7 5 6 7 8

1 2 3 4 5 6 7 8

1 2 3 4 Two angles are consecutive interior angle when they are on the same side and lie inside the two parallel lines. 5 6 7 8

1 2 3 4 Consecutive interior angles ∠3+∠5=180° ∠4+∠6=180° 5 6 7 8

Parallel Lines and Transversals Day 2 Date: 10.10.2018 1. Write down the Essential Question (EQ). 2. Work on the Warm up. Essential Question How does two angles being congruent help you set up the equation? Warm Up: Answer the question What does it mean for ∠1=∠3 𝑜𝑟 ∠2=∠4

Parallel Lines and Transversals Day 3 Date: 10.11.2018 1. Write down the Essential Question (EQ). 2. Work on the Warm up. Essential Question How does two angles being linear pair help you set up the equation? Warm Up: Fill in the blank 65+ =180 80+ =180 2 2 𝑥= 𝑥 5 𝑥=1𝑥

67°+𝑥°=180 They are linear pair 𝑥°=113 𝑦°=113 𝑥°= 𝑦° because they are Alternate exterior angles

109°+𝑥°=180 Consecutives interior angles 𝑥°=71 𝑦°=109 109°= 𝑦° because they are Vertical Angles

90°+𝑥°=180 Consecutives interior angles 𝑥°=90 𝑦°=90 𝑥°+ 𝑦°=180 because they are linear pair

65°+𝑦°=180 They are linear pair 𝑦°=115 𝑥°=65 Corresponding angles

80°+𝑥°=180 They are linear pair 𝑥°=100 𝑦°=80 Alternate exterior angles

𝑥°=130 corresponding angles 𝑦°=130 Vertical Angles

Angles of Triangle Date: 10.12.2018 1. Turn in your homework to the back table. 2. Write down the Essential Question (EQ). 3. Work on the Warm up. Essential Question Why does a triangle have a total of 180° Warm Up: How do all these picture relate?

What is the different?

Vocabulary Interior angles: angle that are inside Exterior angles: angle that are outside

𝟏𝟖𝟎° A line is 𝟏𝟖𝟎°

𝟏𝟖𝟎° Now lets bend the line

𝟏𝟖𝟎°

𝟏𝟖𝟎°

𝟏𝟖𝟎° Notice any thing?

𝟏𝟖𝟎° Nothing happen to the 𝟏𝟖𝟎°

Core Concept B° C° A° Words: The total interior angles measurement of a triangle is 180° Equation: ∠𝐴+∠𝐵+∠𝐶=180°

Find the value of x a. Step 1: Set up an Equation 32°+48°+𝑥°=180° Step 2: Solve for 𝑥 80°+𝑥°=180° −80° −80° 𝑥=100

Find the value of y b. Step 1: Set up an Equation 60°+40°+7°=180° Step 2: Solve for 𝑥 100°+𝑥°=180° −100° −100° 𝑥=80

Find the value of z c. Step 1: Set up an Equation 3𝑧°+(2𝑧+5)°+25°=180° Step 2: Solve for 𝑥 5𝑧+30=180 Combine like terms −30 −30 Subtract 30 to both sides 5𝑧=150 5𝑧 5 = 150 5 𝑧=30 Divide 5 to both sides