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Welcome Back! Collected Warm Up

Welcome Back! Collected Warm Up. Write your name What was your favorite thing you did over break? Think back on all the topics we covered this semester. What topic was most challenging? What topic was most interesting?. Tentative Schedule for End of Semester.

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Welcome Back! Collected Warm Up

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  1. Welcome Back!Collected Warm Up • Write your name • What was your favorite thing you did over break? • Think back on all the topics we covered this semester. • What topic was most challenging? • What topic was most interesting?

  2. Tentative Schedule for End of Semester • Wed 1/2 – Pass out Study Guide Outline, Review problems from Unit 1 • Thurs 1/3 – Work on Study Guide • Fri 1/4 – Review Problems for Unit 2 • Mon 1/7 - Review Problems for Unit 3 • Tues 1/8 - Review Problems for Unit 4 • Wed 1/9 - Review Problems for Unit 5 • Thurs 1/10 - Review Problems for Unit 6 • Fri 1/11 – 3rd Period Final • Mon 1/14 – 2nd Period Final

  3. How can we study for a final?

  4. Today’s Agenda • Work on Unit 1 Test questions • Circle trouble problems • Note easy problems • Review terms and definitions form Unit 1

  5. Review Unit 1

  6. Vocab Review • Point • Line • Plane • Collinear Points • Coplanar Points • Coplanar Lines • Intersection • Line Segment • Ray • Midpoint • Parallel Lines • Congruent Segments • Bisection of a Segment

  7. Solving Line Segments

  8. Solving Line Segments

  9. Pythagorean Theorem

  10. Guided Practice 1. a = 5, b = 12, c = ?

  11. Guided Practice 2. a = 7, c = 25, b = ?

  12. Guided Practice 3. b = 15, c = 17, a = ?

  13. Guided Practice 4. a = 9, b = 12, c = ?

  14. Using Pythagorean Theorem to Find measurement

  15. Review of Angle Vocabulary • Angle • Vertex, Side, Names • Acute Angle • Obtuse Angle • Right Angle • Perpendicular Lines • Complementary Lines • Supplementary Lines • Vertical Angles • Adjacent Angles • Linear Pair

  16. Straight Angles • Definition: (Put in Vocab) A straight angle is an angle whose measure is 180

  17. Interior Points of Adjacent Angles Remember, adjacent angles have a common side and vertex but NO COMMON INTERIOR POINTS

  18. Congruent Angles • If two angles have equal measures, then they are congruent angles • mA = mB ⇔A≅ B A B mA = 40 m B= 40

  19. Angle Bisector • Definition: (Put in Vocab) An angle bisector is a ray that divides an angle into two congruent angles.

  20. Angle Addition Postulate mROS + mSOT = mROT R S O T

  21. Example 1 A Find x, mADB and mBDC 2x+12 D B 82 x+10 C

  22. Example 2 L OM bisects LON 6y-12 O M 108 N

  23. Example 1 • BA  BC 2x -24

  24. Example 2 ABBC mABD = 7x + 2 mDBC = 4x Find x, mABD, and mDBC.

  25. Perpendicular Bisector • What is a segment bisector? • A segment bisector is a line, segment, ray or plane that intersects a segment at its midpoint • Using this definition, what do you think a perpendicular bisector is? • Definition: The Perpendicular Bisector of a segment is a line, segment, or ray that is perpendicular to the segment at its midpoint

  26. Vertical Angle Theorem • If two angles are vertical angles, then they are congruent 2 1 3 4 1 ≅3 and 2≅4

  27. Example 1 (x – 10) 125

  28. Example 2 6x - 45 3x + 21

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