Welcome to the First Day of… UNIT 2!!! Please do the following: Begin your Entry Ticket Homework: Retake Transformation Test Turn in Notes Turn in Transformation Project Updates: 2 mins

Entry Tickets Do this entry ticket to the best of your abilities. I just want to see what you know before we start this unit. 3 mins

Agenda Entry Ticket Fundamentals of Geometry Test Corrections ( Period 1) Types of Angles 1 min

Office Hours At lunch, but you need to tell me if you are coming!! Thursday from 3:15- 4:15 ( no FLEX this week) 3 mins

Points, Lines, and Planes Look around the room. Find a line in the classroom. Be ready to tell us where you found it. Where do you see a point?

1.1 Points, Lines, and Planes The building blocks of geometry are called undefined terms , which cannot be defined by any other figures. These undefined terms are called points, lines, and planes.

1.1 Points, Lines, and Planes

Points, Lines, and Planes How do we use Points, Lines, and Planes in our everyday lives? One way is through maps (Going from Roosevelt to George)! The map is a plane, points represent our starting and ending position, and line creates the path that we take to get from point to point (notice how the lines do not continue forever; they must change direction to make a curve…). George

1.1 Points, Lines, and Planes Say I want to make a couple of stops before going from Roosevelt to George. These stops I make are in a straight line as you see below with red dots. Collinear Points that lie on the same line are collinear. D C

1.1 Points, Lines, and Planes Collinear Points that lie on the same line are collinear. Example: Non-Example

1.1 Points, Lines, and Planes Coplanar Points that lie on the same plane. Since all the points (red or green) lie on the map they are all coplanar. C D

1.1 Points, Lines, and Planes Coplanar Points that lie on the same plane. Example: Non-Example:

1.1 Points, Lines, and Planes Practice: Use the figure to the right to answer each statement. Name one point: Name one line: Name a plane using its script letter and its points  Name three collinear points Name three coplanar points

1.1 Points, Lines, and Planes Let’s go in more detail about a line. In order for lines to change direction they must stop! Therefore, we have a segment which is a part of a line.

1.1 Points, Lines, and Planes In order for lines to change direction they must stop! Therefore, we have a segment which is a part of a line.

1.1 Points, Lines, and Planes If we have a beginning point and just keep traveling in a straight line with no end we have a ray!

1.1 Points, Lines, and Planes (2) Practice: Draw and label each of the following. A segment with endpoints M and N. A ray with endpoint P and another point Q Opposite rays with common endpoint T and points R and S

1.1 Points, Lines, and Planes (3) Practice: Answer the following questions. Name two points: Name two lines: A plane containing E, D, and B. Name three collinear points Name a ray Two Opposite Rays Name a segment. What are its endpoints? A point non-coplanar to plane N.

Summary After each section, you will be required to write 1-2 sentences about something that you learned in this section. “I don’t know” or nothing is not an acceptable answer. It has to be math related. These will be checked when you turn in your notes. Be ready to share out!

Learning Target Tracker Take out your yellow learning target tracker. I am going to give you your tests back! 1 min

Test Corrections NO PHONES! IF I SEE IT, I’ll TAKE IT AWAY FOR THE REMAINDER OF THE DAY. Fix your answers and explain why you made the mistake. You need to fill this out in order to take the reassessment. I have graph paper if you need it. Once done, give it to me and I’ll initial it off. When to retake? Flex days At lunch ( that’s best if you want one on one attention!) After school/ before school 1 min

Test Corrections (Period 1) Students who still need to take the test: Michael Aneesha Kevin Osman 1 min

Test Corrections (Per 5) Students who still need to take the test: Khaleia Kai Cecilia M 1 min

Measuring Angles Take out your whiteboards. On your whiteboard draw what you picture an angle to be. On your whiteboard, shade where the interior of the angle would be. What type of lines create an angle? How do you predict we can name the angle?

1.3 Measuring Angles Vertex Formed by two rays (in this case, RS and RT), or sides, with a common endpoint (in this case R). Naming an angle By the vertex Can only do this if you have a single angle (it cannot be connected to another). A point on a ray, the vertex, followed by a point on the second ray. Can do this with any angle. By a number If a number is given on the interior of an angle. R 1

1.3 Measuring Angles (1) Practice: Write all the different ways you can name the angles in the diagram.

1.3 Measuring Angles Now that we can name any given angle, lets look at the types of angles!

Whiteboards On your whiteboard identify if the measure of the angle is acute, right, obtuse, or straight. 59° 89° 180° 1° 156° 90°

Notecards! I want you to begin writing notecards for the terms you learned today. If you need help first ask your tablemates and then ask me. FRONT: -Vocab work BACK: - Picture of the word and the definition

1.3 Measuring Angles To measure any angle we use a protractor! http://www.youtube.com/watch?v=SBtojUG1z6s

1.3 Measuring Angles How to read a protractor Place the bottom center of your protractor at the vertex of your angle. Make sure the line on the bottom overlaps one ray of your angle. Note the angle that the second ray is going to. Identify if the angle is acute, obtuse, or right and choose the appropriate degree.

1.3 Measuring Angles (2) Practice: Find the measure of each angle. Then classify each as acute, right, obtuse, or straight. (a) ∠ WXV (b) ∠ ZXW (c) ∠ YXW (d) ∠ YXV

1.3 Measuring Angles There are times when we will have angles with the same shape and size. What do you predict these types of angles are? Congruent Angles Angles that have the same measure. Angles that have the same size and same shape. Arc marks are used to show that angles are congruent. For the diagram to the right we would say ∠ABC ≅ ∠DEF.

1.3 Measuring Angles You will commonly see m∠ABC = m∠DEF which denotes that the angles have the same measure. Note – congruence demonstrates same size and shape while an equal sign denotes actual numbers are involved, hence measurement.

1.3 Measuring Angles Lets look at (3) (a), take one minute to label the information on your diagram. Discuss in your groups an action plan. How would you find mFEG ?

You just used the angle addition postulate!! 1.3 Measuring Angles You just used the angle addition postulate!!

1.3 Measuring Angles (3) Practice: Attempt the following problems. (a) mDEG = 115°, and mDEF = 48°. Find mFEG. (b) mXWZ = 121° and mXWY = 59°. Find mYWZ.

1.3 Measuring Angles What do you picture an angle bisector to be? A ray that divides an angle into two congruent angles. JK bisects LJM; thus LJK  KJM.

1.3 Measuring Angles (4) Practice: KM bisects JKL, mJKM = (4x + 6)°, and mMKL = (7x – 12)°. Find mJKM.

Whiteboards How can we tell if angles are congruent?

Whiteboards Explain why any two right angles are congruent.

Summary After each section, you will be required to write 1-2 sentences about something that you learned in this section. “I don’t know” or nothing is not an acceptable answer. It has to be math related. These will be checked when you turn in your notes. Be ready to share out!