1. Sabin Tanner Jina Sam R Tyler Taylor Connor Kevin Elaina Sophia Sam B Dhimitri Jessica Sydney Jamie CJ Josh Shawn Amanda Michael Nick Ben Ramsey Noah Ted Kirstin Will

2. Tyler Alex Jake Madeline Taylor Andrew Shane Reganne Colin Emmy Ben Arthur Jack Rachel Hunter Ryan Amanda Mari Kearstin Becca Miranda

3. 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500 100 200 300 400 500 Inductive vs. Deductive ProofsJustify! Condi- tionals Definitions

4. Conditionals - 100 Identify the hypothesis of the following conditional statement: If m  ABC = 20, then  ABC is an acute angle. Answer: m  ABC = 20.

5. Conditionals - 200 State the converse of this conditional: If m  ABC = 20, then  ABC is an acute angle. Answer: If  ABC is an acute angle, then m  ABC = 20.

6. Conditionals - 300

7. Conditionals - 400 Provide a counterexample to demonstrate why the converse of this statement is false. If m  ABC = 20, then  ABC is an acute angle. Answers may vary: m  ABC could equal any number between 0 and 90.

8. Conditionals - 500 Rewrite the definition of complementary angles as a biconditional statement. Complementary angles – two angles whose measures sum to 90°. Answer: Angles are complementary if and only if the sum of their measures is 90°.

9. Definitions - 100

10. Definitions - 200 State the definition of perpendicular lines. Answer: Perpendicular lines are intersecting lines that meet to form right angles.

11. Definitions - 300 State the definition of a right angle. Answer: A right angle is an angle that measures 90°.

12. Definitions - 400 Which of the following is the definition of a midpoint: A.) If point B is the midpoint of AC, then AB = BC. B.) If point B is the midpoint of AC, then AB = ½AC. C.) If point B is the midpoint of AC, then DB bisects AC. D.) If BX bisects  ABC, then  ABX   XBC. Answer: A: If point B is the midpoint of AC, then AB = BC.

13. Definitions - 500 What is the reason that you could use in a proof to justify that  1   2. 1 2 Answer: Vertical Angle Theorem – “Vertical Angles are Congruent.”

14. Justify! - 100 Look at the diagram and provide a justification (property, postulate, definition, or theorem) that allows you to reach the conclusion stated. B D C F G X 1 3 2 DX + XF = DF Answer: Segment Addition Postulate.

15. Justify! - 200

16. Justify! - 300 Look at the diagram and provide a justification (property, postulate, definition, or theorem) that allows you to reach the conclusion stated. B D C F G X 1 3 2 If  CXF and  DXG are supplementary, then m  CXF + m  DXG = 180 Answer: Def. of Supplementary Angles.

17. Justify! - 400 Look at the diagram and provide a justification (property, postulate, definition, or theorem) that allows you to reach the conclusion stated. B D C F G X 1 3 2 If m  BXD + m  DXG = m  FXG + m  DXG, then m  BXD =  FXG. Answer: Subtraction Property.

18. Justify! - 500 Look at the diagram and provide a justification (property, postulate, definition, or theorem) that allows you to reach the conclusion stated. B D C F G X 1 3 2 If XF bisects  CXG, then m  CXF = ½m  CXG. Answer: Angle Bisector Theorem.

19. Proofs - 100 Fill in the missing piece to the proof. StatementsReasons 1. m  1 = m  21. Given 2. m  1 = m  3 2. Vertical Angles are  3. ___________3. Substitution m  2 = m  3

20. Proofs - 200 Fill in the missing pieces to the proof. 1 2 3 4 A BC Given: m  ABC =  m  ACB, m  1 = m  3 Prove: m  2 = m  4 StatementsReasons 1. m  ABC =  m  ACB1 2. m  1 + m  2 = m  ABC m  3 + m  4 = m  ACB 2 3. m  1 + m  2 = m  3 + m  43 4. m  1 = m  34 5. m  2 = m  45 Given  Add. Post. Substitution Given Subtraction

21. Proofs - 300 Fill in the missing pieces to the proof. A B C D X 1 2 3 Given: m  AXC = m  BXD Prove: m  1  =  m  3 StatementsReasons 1. m  AXC = m  BXD1. Given 2. ____________________ 2.  Add. Postulate ____________________ 3. m  1 + m  2 = m  2 + m  33. _____________ 4. m  1 = m  34. _____________ m  1 + m  2 = m  AXC m  2 + m  3 = m  BXD Substitution Subtraction

22. Proofs - 400

23. Proofs - 500 Complete the proof. StatementsReasons ABC F ED Given: AC = DF; AB = EF Prove: BC = DE 1. AC = DF 2. AB + BC = AC DE + EF = DF 3. AB + BC = DE + EF 4. AB = EF 5. BC = DE 1. Given 2. Segment Addition Postulate 3. Substitution 4. Given 5. Subtraction

24. Inductive vs. Deductive - 100 You notice that the 6 pentagons you have drawn on your paper has interior angle measures that add up to 540 °. You conclude that all pentagons have interior angle measures that add up to 540 °. Answer: Inductive

25. Inductive vs. Deductive - 200 When you complete a proof what type of reasoning are you applying? Answer: Deductive

26. Inductive vs. Deductive - 300

27. Inductive vs. Deductive - 400 When you complete an experiment that consists of making observations and then drawing conclusions, what type of reasoning are you applying? Answer: Inductive

28. Inductive vs. Deductive - 500 Just for fun… Look for a pattern and predict the next two numbers in the sequence. 12, 14, 18, 24, ____, ____, … Answer: 32, 42

29. FINAL JEOPARDY Category: Planning a Proof Place your wagers!