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Agenda

Agenda. Put 2.2 homework on the board while I check homework Go over 2.2 homework 2.3 – Definitions What makes a statement a definition?. 2.3 – Definitions. Geometry 2010 – 2011. Consider this…. Why do people have disagreements?

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Agenda

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  1. Agenda • Put 2.2 homework on the board while I check homework • Go over 2.2 homework • 2.3 – Definitions • What makes a statement a definition?

  2. 2.3 – Definitions Geometry 2010 – 2011

  3. Consider this… • Why do people have disagreements? • Different meanings are assigned to the same word, phrase, statement. • Why is it important in mathematics to know the definitions of the terms used?

  4. What are floppers? • Observe the differences in the figures in card 1 and card 2 (also on page 99 in the text). Which figures on card 3 are floppers? • Write a definition for a “flopper” using a conditional statement. • Write the converse of the conditional you wrote in #2. • Is the conditional from #2 true or false? (counterexample if false) • Is the converse from #3 true or false? (counterexample in false)

  5. Classifying These Statements 6. A definition is a conditional statement having the property that both it and its converse are true. 7. Combine the two true statements from #2 and #3 using the phrase “if and only if.” 8. A statement using the phrase “if and only if” is known as a biconditional. 9. In logical notation, the statement p if and only if q can be written symbolically as __________. This is read as p if and only if q.

  6. Diamond is a very hard rock. • Write the sentence as a conditional statement. • Write the converse of the conditional. • Write a biconditional statement. • Decide whether the sentence is a definition, and explain your reasoning.

  7. What are adjacent angles? • Examine the figures below (also shown on page 101 in your textbook) to form an idea of what adjacent angles are and are not.

  8. Now apply your observations. 11. List the pairs of adjacent angles. 12. What do adjacent angles have in common? Can they overlap?

  9. Adjacent Angles 13. Angles that do not overlap have no interior points in common. Adjacent anglesare angles in a plane that have their vertices and one side in common but no interior points in common.

  10. Homework • Page 103 #8 – 16 (even), 17 – 22, 24 – 28, 30 – 38

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