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

2. GEOMTRY GAME PLAN DateMonday, 9/23/13 Section / Topic2.1 Conditional Statements Lesson Goal Students will be able to recognize and analyze conditional statements. Standard Geometry California Standard 4.0 Students prove basic theorems involving congruence. Homework Per 4: Khan Academy Per 6: Page 75: 9 – 21, 63 – 66 Announcement Late Start on Wednesday

3. 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 after the word “If” Conclusion is the part after the word “then”

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

5. 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

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

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

8. 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.

9. 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.

10. 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.

11. Negation Writing the opposite of a statement. Ex: negate x=3 x≠3 Ex: negate t>5 t 5

12. Inverse Negate the hypothesis & conclusion of a conditional statement. Ex: Write the inverse of: “If you are a brunette, then you have brown hair.” If you are not a brunette, then you do not have brown hair.

13. Contrapositive Negate, then switch the hypothesis & conclusion of a conditional statement. Ex: Write the contrapositive of: “If you are a brunette, then you have brown hair.” If you do not have brown hair, then you are not a brunette.

14. The original conditional statement & its contrapositive will always have the same meaning. The converse & inverse of a conditional statement will always have the same meaning.

15. Remember that postulates are assumed to be true—they form the foundation on which other statements (called theorems) are built.

17. Postulate 5: Through any two points exists exactly one line.

18. GEOMTRY GAME PLAN DateMonday, 9/23/13 Section / Topic2.1 Conditional Statements Lesson Goal Students will be able to recognize and analyze conditional statements. Standard Geometry California Standard 4.0 Students prove basic theorems involving congruence. Homework Page 75: 9 – 21, 63 – 66 Announcement Late Start on Wednesday