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9/23/13 Warm Up

9/23/13 Warm Up . Q is between P and R . PQ = 2 w – 3 and QR = 4 + w, and PR = 34. Find the value of w , PQ , AND QR. Use the diagram to find the measures of angles 4 & 5. 68˚. Conditional Statement. A logical statement with 2 parts

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9/23/13 Warm Up

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  1. 9/23/13 Warm Up • Q is between P and R. PQ = 2w – 3 and QR = 4 + w, and PR = 34. Find the value of w, PQ, AND QR. • Use the diagram to find the measures of angles 4 & 5. 68˚

  2. Conditional Statement • A logical statement with 2 parts • 2 parts are called the hypothesis & conclusion • Can be written in “if-then” form; such as, “If…, then…” • Hypothesis is the part afterthe word “If” • Conclusion is the part afterthe word “then”

  3. Ex: Underline the hypothesis & circle the conclusion. • If you are a brunette, then you have brown hair. hypothesis conclusion If two points lie on the same line, then they are collinear.

  4. Rewrite the statement in “if-then” form Ex 1: Vertical angles are congruent. If there are 2 vertical angles, then they are congruent. If 2 angles are vertical, then they are congruent. Ex 2: An object weighs one ton if it weighs 2000 lbs. If an object weighs 2000 lbs, then it weighs one ton. Ex 3: All monkeys have tails. If an animal is a monkey, then it has a tail

  5. Counterexample • Used to show a conditional statement is false. • It must keep the hypothesis true, but the conclusion false!

  6. Write a counterexample to prove the statement is false. Ifx2 = 81, thenx must equal 9. Counterexample: x could be (-9) because (-9)2=81, but x≠9. The hypothesis true, but the conclusion false!

  7. Counterexample Write a counterexample for the following statements: 1) If a number is divisible by 2, then it is divisible by 4. Counterexample: 10 is divisible by 2 but not 4. 2) If a bird is a swan, then it is white. Counterexample: A swan can also be black.

  8. Converse • Switch the hypothesis & conclusion parts of a conditional statement. • Ex: Write the converse of: • “If you are a brunette, then you have brown hair.” If you have brown hair, then you are a brunette.

  9. Write the CONVERSE of the statement 1) If there is snow on the ground, then flowers are not in bloom. Converse: If flowers are not in bloom, then there is snow on the ground. 2) If two segments are congruent, then they have the same measure. Converse: If segments have the same measure, then they are congruent.

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