Do Now: Find the distance between the following points: (12,12) and (-3,1). Then find the distance between (1,-9) and (6, -6)

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Presentation transcript:

Do Now: Find the distance between the following points: (12,12) and (-3,1). Then find the distance between (1,-9) and (6, -6)

Objective SWBAT name, measure, and classify angles.

What is an angle? An angle is formed by two rays with a common endpoint. The common endpoint is called a vertex. The two rays are called the sides of an angle

CFU #1 What is a vertex? A.A side B.A ray C.An endpoint

How do we name an angle? Angles are named by naming a point on one side, then the vertex, then a point on the other side.

It doesn’t matter which side you start with as long as the vertex is in the middle!

CFU #2 How many angles can you name in the picture below?

Protractor Postulate Angles are measured with something called a protractor. A protractor is a measuring device that measures how “open” an angle is. Angles are measured in degrees, and labeled with a ⁰ symbol.

How to use a protractor

What is the measure of the angle shown ?

Classifying Angles Angles that measure less than 90⁰ are called acute angles. Angles that measure exactly 90⁰ are called right angles. Angles that measure more than 90⁰ are called obtuse angles. Angles that measure exactly 180 ⁰ are called straight angles.

Is it acute, right, obtuse, or straight?

Angle Addition Postulate First, let’s recall some previous information from last week…. We discussed the Segment Addition Postulate, which stated that we could add the lengths of adjacent segments together to get the length of an entire segment. For example: JK + KL = JL If you know that JK = 7 and KL = 4, then you can conclude that JL = 11. The Angle Addition Postulate is very similar, yet applies to angles. It allows us to add the measures of adjacent angles together to find the measure of a bigger angle… JKL

Angle Addition Postulate 50  65  A B C O If B lies on the interior of  AOC, then m  AOB + m  BOC = m  AOC. m  AOC = 115 

Example 1 G H J K Given: m  GHK = 95 m  GHJ = 114. Find: m  KHJ. The Angle Addition Postulate tells us: m  GHK + m  KHJ = m  GHJ 95 + m  KHJ = 114 m  KHJ =  114  19  Plug in what you know. Solve.

R S T V Given: m  RSV = x + 5 m  VST = 3x - 9 m  RST = 68 Find x. m  RSV + m  VST = m  RST x x – 9 = 68 4x- 4 = 68 4x = 72 x = 18 Set up an equation using the Angle Addition Postulate. Plug in what you know. Solve. Extension: Now that you know x = 18, find m  RSV and m  VST. m  RSV = x + 5 m  RSV = = 23 m  VST = 3x - 9 m  VST = 3(18) – 9 = 45 Check: m  RSV + m  VST = m  RST = 68

B Q D C m  BQC = x – 7 m  CQD = 2x – 1 m  BQD = 2x + 34 Find x, m  BQC, m  CQD, m  BQD. m  BQC + m  CQD = m  BQD 3x – 8 = 2x + 34 x – 7 + 2x – 1 = 2x + 34 x – 8 = 34 x = 42 m  BQC = 35 m  CQD = 83 m  BQD = 118 x = 42 m  BQC = x – 7 m  BQC = 42 – 7 = 35 m  CQD = 2x – 1 m  CQD = 2(42) – 1 = 83 m  BQD = 2x + 34 m  BQD = 2(42) + 34 = 118 Check: m  BQC + m  CQD = m  BQD = 118

Guided Practice Complete questions 1 through 8 in groups. Be prepared to review the questions in front of the class.

Independent Practice On a sheet of loose leaf paper. Complete questions 9 through 12 using the statement/ reason method. Your final answers should be boxed and the value of each angle should be clearly marked. This portion of the class should be silent. If you have a question that you must ask a neighbor, please be sure to whisper.