2. Welcome to Interactive Chalkboard Glencoe Geometry Interactive Chalkboard Copyright © by The McGraw-Hill Companies, Inc. Developed by FSCreations, Inc., Cincinnati, Ohio 45202 Send all inquiries to: GLENCOE DIVISION Glencoe/McGraw-Hill 8787 Orion Place Columbus, Ohio 43240

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6. Contents Lesson 2-1Inductive Reasoning and Conjecture Lesson 2-2Logic Lesson 2-3Conditional Statements Lesson 2-4Deductive Reasoning Lesson 2-5Postulates and Paragraph Proofs Lesson 2-6Algebraic Proof Lesson 2-7Proving Segment Relationships Lesson 2-8Proving Angle Relationships

7. Lesson 4 Contents Example 1Determine Valid Conclusions OBJECTIVE: To use the Law of Detachment (2.8.11Q) (M8.D.1.1) KEY CONCEPT: Law of Detachment (conditional must be true). If p -> q is TRUE and p is TRUE, then q is also TRUE. [(p -> q) ^ p] -> q.

8. Example 4-1a The following is a true conditional. Determine whether the conclusion is valid based on the given information. Explain your reasoning. If two segments are congruent and the second segment is congruent to a third segment, then the first segment is also congruent to the third segment. Conclusion: The hypothesis states that Answer: Since the conditional is true and the hypothesis is true, the conclusion is valid. Given:

9. Example 4-1b The following is a true conditional. Determine whether the conclusion is valid based on the given information. Explain your reasoning. If two segments are congruent and the second segment is congruent to a third segment, then the first segment is also congruent to the third segment. Answer: According to the hypothesis for the conditional, you must have two pairs of congruent segments. The given only has one pair of congruent segments. Therefore, the conclusion is not valid. The hypothesis states that is a segment and Conclusion: Given:

10. Example 4-1c The following is a true conditional. Determine whether each conclusion is valid based on the given information. Explain your reasoning. If a polygon is a convex quadrilateral, then the sum of the interior angles is 360. a. Given: Conclusion: If you connect X, N, and O with segments, the figure will be a convex quadrilateral. b. Given: ABCD is a convex quadrilateral. Conclusion: The sum of the interior angles of ABCD is 360. Answer: not valid Answer: valid

11. Review Determine whether the stated conclusion is valid based on the given information. If not, write invalid. Explain your reasoning. 1.Given:  A and  B are vertical angles. Conclusion: 2.Given: Conclusion:  C and  D are vertical angles. VALID INVALID; congruent angles do not have to be vertical.

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