Section 2.1 Conditional Statements Chapter 2 Section 2.1 Conditional Statements

Warm-Up Name a point collinear with N and U. Name a point coplanar with L, M, R. Name a point coplanar with L, M, N. 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 It is time for dinner if it is 6 pm. There are 12 eggs if the carton is full A number is divisible by 6 if it is divisible by 2 and 3. An obtuse angle is an agle that measures more than 90 and less than 180. 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 x2 = 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 Decide whether the statement is true or false. If it is false, give a counter example The equation 4x – 3 = 12 + 2x has exactly one solution If x2 = 36 then x = 18 or x = -18 Thanksgiving is celebrated on a Thursday If you’ve visited Springfield, then you’ve been to Illinois. 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 If you like hockey, then you go to the hockey game If x is odd, then 3x is odd 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 see lightning, then you do not hear thunder If you like hockey, then you go to the hockey game If x is odd, then 3x is odd 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 see lightning If you like hockey, then you go to the hockey game If x is odd, then 3x is odd If mP = 90, then P is a right angle

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

Point, Line, and Plane Postulates Through any two points there exists exactly one line A line contains at least two points If two lines intersect, then their intersection is exactly one point (14) Through any three noncollinear points there exists exactly one one plane

Point, Line, and Plane Postulates A plane contains at least three noncollinear points If two points lie in a plane, then the line containing them lies in the same plane (15) If two planes intersect, then their intersection is a line. (16)

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

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