Chapter 2

Section 2.1

Conditional Statements

Warm-Up 1. Name a point collinear with N and U. 2. Name a point coplanar with L, M, R. 3. Name a point coplanar with L, M, N. 4. Name a point coplanar with S, P, Q.

Conditional Statement

• • • • Type of logical statement 2 parts – Hypothesis/Conclusion Usually written in “if-then” form If George goes to the market , then he will buy milk.

Hypothesis Conclusion

If the hypothesis is true then the conclusion must be true

Rewrite each conditional statement in if-then form 1. It is time for dinner if it is 6 pm.

2. There are 12 eggs if the carton is full 3. A number is divisible by 6 if it is divisible by 2 and 3.

4. An obtuse angle is an agle that measures more than 90 and less than 180.

5. All students taking geometry have math during an even numbered block

Counter Example

• • Used to prove a conditional statement is false Must show an instance where the hypothesis is true and the conclusion is false.

– – Ex. If x 2 = 9 then x = 3 Counter Ex. (-3) 2 = 9, but –3,  3 • Only need one counter example to prove something is not always true.

Decide whether the statement is true or false. If it is false, give a counter example 6. The equation 4x – 3 = 12 + 2x has exactly one solution 7. If x 2 = 36 then x = 18 or x = -18 8. Thanksgiving is celebrated on a Thursday 9. If you’ve visited Springfield, then you’ve been to Illinois.

10. Two lines intersect in at most one point.

• New statements formed from a conditional – – Converse: Switch the hypothesis and conclusion Conditional: If you see lightning , then you hear thunder Converse: If you hear thunder , then you see lightning 11. If you like hockey , then you go to the hockey game 12. If x is odd , then 3x is odd 13. If m  P = 90 , then  P is a right angle

New statements formed from a conditional • • Inverse: When you negate the hypothesis and conclusion of a conditional – Negate: To write the negative of a statement Conditional: If you see lightning , then you hear thunder – Inverse: If you do not thunder see lightning , then you do not hear 11. If you like hockey , then you go to the hockey game 12. If x is odd , then 3x is odd 13. If m  P = 90 , then  P is a right angle

New statements formed from a conditional • – Contrapositive: When you switch and negate the hypothesis and conclusion of a conditional Conditional: If you see lightning , then you hear thunder – Contrapositive: If you do not hear thunder , then you do not lightning see 11. If you like hockey , then you go to the hockey game 12. If x is odd , then 3x is odd 13. If m  P = 90 , then  P is a right angle

Equivalent Statements

• When two statements are both true, they are called equivalent statements Original Inverse Converse Contrapositive If m  A = 30, then  A is acute If m  A  30, then  A is not acute If  A is acute, then m  A = 30 If  A is not acute, then m  A  30

Point, Line, and Plane Postulates

5. Through any two points there exists exactly one line 6. A line contains at least two points 7. If two lines intersect, then their intersection is exactly one point (14) 8. Through any three noncollinear points there exists exactly one one plane

Point, Line, and Plane Postulates

9. A plane contains at least three noncollinear points 10. If two points lie in a plane, then the line containing them lies in the same plane (15) 11. If two planes intersect, then their intersection is a line. (16)

Use the diagram to state the postulate that verifies the statement 17. The points E, F, and H lie in a plane 18. The points E and F lie on a line

Use the diagram to state the postulate that verifies the statement 19. The planes Q and R intersect in a line 20. The points E and F lie in plane R. Therefore, line m lies in plane R