Reasoning and Proof. 2.3 . Agenda. Check your skills Homework Check 2-3 Notes Practice Homework/work on Projects. Check your skills. If a point is in the third quadrant then the coordinates are negative. Write the converse: Write the inverse: Write the contrapositive.
If a point is in the third quadrant then the coordinates are negative.
1. If today is Friday, then tomorrow is Saturday.
a. Today is Friday b. Tomorrow is Saturday
2. The car will not start, if the battery is discharged. (hint: rearrange the order)
3. Alligators are reptiles. If it is an alligator then it is a reptile.
4. College students work diligently. If a person is a college student then they work diligently.
converse: If angles’ are supplementary, then the two angles’ sum is 180.
inverse: If two angles’ sum is not 180, then the two angles are not supplementary.
contrapositive: If two angles are not supplementary then their sum is not 180.
6. If two angles are a vertical, then they are congruent.
converse: If two angles are congruent, then the two angles are vertical.
inverse: If two angles are not a vertical pair then they are not congruent.
contrapositive: If two angles are not congruent, then they are not a vertical pair
converse: If tomorrow is not Wednesday, then today is not Tuesday.
inverse: If today is Tuesdays, then tomorrow is Wednesday.
contrapositive: If tomorrow is Wednesdays, then today is Tuesday.
8. If two lines are parallel, then they do not intersect.
Converse: If two lines do not intersect, then they are parallel. False
Counterexample: Skew lines – do not intersect and are not parallel.
Biconditional: Two lines are skew if and only if they are noncoplanar.
A biconditional combines p → q and q → p as p ↔ q.
When a conditional and its converse are true, you can combine them as a true biconditional. This is a statement you get by connecting the conditional and its converse with the word and.
You can also write a biconditional by joining the two parts of each conditional with the phrase if and only if
Law of Detachment: If a conditional is true and its hypothesis is true, then its conclusion is true.
If p q is a true statement and p is true, then q is true
**Do not need to know terminology but must be able to apply the laws
Use the Law of Detachment to draw a conclusion. If it is not possible to draw a conclusion based on the given information write not possible
The measure of angle A is greater than 90⁰.
Cannot draw a conclusion. You are only told the conclusion of the statement above is true.
Law of Syllogism: If p q and q r are true statements, then p r is a true statement.
** Do not need to know terminology but must be able to apply the law.
3. If angles are a linear pair,
then they are supplementary.
If angles are supplementary,
then their sum is 180⁰.
If angles are a linear pair then their sum is 180⁰.
You may work in Groups but I need one paper per person turned in for a classwork grade!
Scrapbook project due Friday
Distance/Midpoint mini-project due Tues. 9/18