Welcome Geometry!

1. Please do the following: Pick up Entry Ticket from the side shelf. Take out HW #4 and #5. Homework: HW #6 Pg. 24 #4-10, 27, 29-32 Updates: Unit 1 Quiz 2 is Wednesday/Thursday (1.1-1.4, 3.1) Welcome Geometry! 3° Due – 8/26 4° Due – 8/25

2. Agenda • Entry Ticket • Review HW #4 and #5 • Finish U1L3 • Notecards (if time) • Unit 1 Quiz 1 – (Pass back materials)

3. Entry Ticket

4. Review HW #4 and #5

5. Learning Objective By the end of this period you will be able to: • Name and classify angles.

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

7. 1.3 Measuring Angles To measure any angle we use a protractor! http://www.youtube.com/watch?v=SBtojUG1z6s

8. 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.

9. 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

10. 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 tic marks are used to show that angles are congruent. For the diagram to the right we would say ∠ABC ≅ ∠DEF.

11. 1.3 Measuring Angles You will commonly see m∠ABC= m∠DEFwhich 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.

12. 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 ?

13. 1.3 Measuring Angles You just used the angle addition postulate!!

14. 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.

15. 1.3 Measuring Angles Last class period we discussed briefly about a bisector. What do you picture an angle bisector to be? Angle Bisector • A ray that divides an angle into two congruent angles. • JK bisects LJM; thus LJKKJM.

16. 1.3 Measuring Angles (4) Practice: KM bisects JKL, mJKM = (4x + 6)°, and mMKL = (7x – 12)°. Find mJKM.

17. Unit 1 Quiz 1 Put everything under your desk or in your backpack. All you need is a pencil and eraser. Please put up your testing shields. You will only be given 20 minutes to complete. As you are taking the quiz, I will be passing back some of your work.

18. Constructing Segments and Angles How can we apply what we are doing in the classroom to outside and in the real world? Through Constructions!! Constructions • A way of creating a figure that is more precise. • One way to make a geometry construction is to use a compass, protractor, and straightedge.

19. Constructing Segments and Angles

20. Constructing Segments and Angles

21. Constructing Segments and Angles http://www.youtube.com/watch?v=i0MsRc9Pzeg This video is going to show you some of the most amazing structures we have created throughout the years. In order to begin building these types of structures we will start from the foundation. In this period we are going to construct: • Congruent Segments • Sum/Difference/Product of Segments • Segment Bisectors • Congruent Angles • Angle Bisectors

22. Constructing Segments and Angles When constructing any figures in this class do NOT erase arcs or lines; this is showing your work.