September 25, 2015
(2.3) Conditional Statements
Objective: To analyze statements in "if-then" form and write the
converse, inverse, and contrapositive of conditional statements.
Why: To broaden your ability to reason logically
September 25, 2015
Obj: To analyze statements in "if-then" form and write the
converse, inverse, and contrapositive of conditional statements.
Conditional Statement:
If we do not have geometry class, then I will be sad.
September 25, 2015
Obj: To analyze statements in "if-then" form and write the
converse, inverse, and contrapositive of conditional statements.
Identify the hypothesis and the conclusion of the conditional stmt.
1. If a polygon has seven sides, then it is a heptagon.
2. Tammy will advance to the next level if she completes the maze
in her computer game.
September 25, 2015
Obj: To analyze statements in "if-then" form and write the
converse, inverse, and contrapositive of conditional statements.
Rewrite in "if-then" form. Then identify the hypothesis and
conclusion.
Cats have whiskers.
"If-then" form: ___________________________________
hypothesis: __________________________
conclusion: ___________________________
The sum of the measures of two supplementary angles is 180o.
"If-then" form: ___________________________________
hypothesis: __________________________
conclusion: ___________________________
September 25, 2015
Obj: To analyze statements in "if-then" form and write the
converse, inverse, and contrapositive of conditional statements.
Truth Table for a Conditional Statement
September 25, 2015
Obj: To analyze statements in "if-then" form and write the
converse, inverse, and contrapositive of conditional statements.
The hypothesis and conclusion of a conditional stmt. can have a
truth value of T or F.
If Tom finishes his homework, then he will clean his room.
September 25, 2015
Obj: To analyze statements in "if-then" form and write the
converse, inverse, and contrapositive of conditional statements.
Determine the truth value of each conditional stmt. If F, give a
counterexample.
1. If you subtract a whole number from another whole number,
the result is also a whole number.
2. When a rectangle has an obtuse angle, it is a parallelogram.
"If-then" form: ____________________________________
September 25, 2015
Related Conditionals:
p: a figure is a square
q: a figure is a rectangle.
conditional:
p
converse:
inverse:
contrapositive:
q
Obj: To analyze statements in "if-then" form and write the
converse, inverse, and contrapositive of conditional statements.
September 25, 2015
September 25, 2015
Obj: To analyze statements in "if-then" form and write the
converse, inverse, and contrapositive of conditional statements.
Logically equivalent: Statements with the same truth value.
September 25, 2015
Obj: To analyze statements in "if-then" form and write the
converse, inverse, and contrapositive of conditional statements.
Write the conditional in "if-then" form. Then write the converse,
inverse, and contrapositive. Determine the truth value for each.
Squares are rectangles.
conditional:
converse:
inverse:
contrapositive:
September 25, 2015
Biconditional Statement:
Obj: To analyze statements in "if-then" form and write the
converse, inverse, and contrapositive of conditional statements.
(statement in which the Conditional AND the Converse are true)
Cond: If an angle is bisected, then it divides the angle into 2 congruent angles.
Conv: If an angle is divided into 2 congruent angles, then it has been bisected.
An angle is bisected IFF it is divided into 2 congruent angles.
September 25, 2015
Obj: To analyze statements in "if-then" form and write the
converse, inverse, and contrapositive of conditional statements.
HW:
(HR) (2.3) Pg.111: 21, 23, 27, 29, 31, 39, 42, 43, 45, 59-61
and Pg.116: 1, 4