Geometry June 19, 2008 1st Qtr

Are the ff. statements true? Justify.
1) If a student scored higher than 95%, then the student earns an A.
FALSE, 95% and up is equivalent to an A+.

2) If 12+3=15, then 15-12=3.
TRUE, APE.

3) If 3x-7=3, then x=4.
FALSE, x=10/3.

4) If a person gets measles vaccination, then that person will not get measles.
FALSE, measles vaccination prevents a person to have measles, but not entirely measles-free.

CONDITIONALS
> statements written in " if - then " form
If - hypothesis
then - conclusion

e.g.
If you live in a mansion, then you have a big heating bill.

EXERCISES:
A. Change to "if-then" form. Encircle the hypothesis & underline the conclusion
1. All right angels are congruent.

"If all angles are right, then they're all congruent."

2. Vertical Angels are congruent.

"If all angles are vertical, then they're all congruent."

3. The sum of 2 even numbers is even.

"If 2 even numbers are added, then the sum would be even."

4. The measure of an obtuse angle is greater than 90 degrees, but less than 180 degrees.

"If it is an obtuse angle, then the measure of the angle is greater than 90 degrees but less than 180 degrees."

B. Add info to the hypothesis in order to make the conditional true.

1. If a number is a perfect square, then the square root is even.

"If an even number is a perfect square, then the square root is even."

2. If 2 angles are supplementary, then one is acute & one is obtuse.

If 2 angles are supplementary which is equal to 180 degrees, then one is acute & one is obtuse.

TRUTH TABLE

Hypothesis : T F T F

Conclusion: T T F F

Condition: T F F T
"If 12+3 = 15, then 15-12=3"

"If 12+3>< 12="3" style="color: rgb(51, 102, 255);">"If measurement of angle P (90 degrees), then measurement of angle P is obtuse."

"If 12+3><15,><>

Kinds of Conditionals

CONVERSE
- formed by "interchanging the hypothesis & the conclusion"

e.g.
before : If the moon is full, then the vampires are prowling.
after: If the vampires are prowling, then the moon is full.

BICONDITIONAL
- conditional & converse both true
- uses 'if and only if' statement instead of if-then

e.g.
before: If points are collinear then they are contained on the same line.
after: Points are collinear if and only if they are contained on the same line.

INVERSE
- formed by negating the hypothesis & the conclusion
-Not, ><

e.g.
before: If it rains, then I do not go fishing
after: If it does not rain, then I go fishing

CONTRAPOSITIVE
- formed by negating the hypothesis & the conclusion of its converse
- negate a converse


e.g.
before: If you understand logic, you will be a good consumer.
after: If you're not a good consumer, the you don't understand logic.


* STATEMENTS: If angles are right, then they are congruent.
CONVERSE: If the angles are congruent, the angle's are right.
BICONDITIONAL: Angels are right if and only if they are congruent.
INVERSE: If angles are not right, then they are not congruent.
CONTRAPOSITIVE: If they are not congruent, then angles are not right.