Download presentation

1
**2.1.4 USING LOGICAL REASONING**

Logical reasoning is based on conditionals. A CONDITIONAL is an if-then statement HYPOTHESIS: The part following the “if” CONCLUSION: The part following the “then” EX: If I live in Dallas HYPOTHESIS If I live in Dallas then I must be a Mavericks fan CONCLUSION then I must be a Mavericks fan

2
**CONDITIONALS CAN BE TRUE OR FALSE**

TRY WRITING THE FOLLOWING STATEMENTS AS CONDITIONALS (IF-THEN STATEMENTS), and identify the hypothesis and conclusion in each. 1) Vertical angles are congruent. 2) October has 31 days 3) Two lines parallel to a third line are parallel to each other.

3
**PRACTICE WITH CONCLUSIONS**

What can you conclude? 1) If <A is a right angle then A B C 2) 4 1 2 3

4
What can you conclude? 3) a. If M is the midpoint of DE then b. If XM is the perpendicular bisector of DE then M E D X

5
**COUNTEREXAMPLE – A particular example or instance of the statement that is not true**

CONDITIONAL: If a month has thirty days, then it is September COUNTEREXAMPLE: April The month must have thirty days but could not be September. Try this one! CONDITIONAL: If you live in a state that begins with C, then you live in a state that does not border the ocean COUNTEREXAMPLE: California

6
**CONVERSE – Interchanges the hypothesis and the conclusion**

CONDITIONAL: If it is noon, then it is time to eat lunch. CONVERSE: If it is time to eat lunch, then it is noon.

7
**CONVERSES CAN BE TRUE OR FALSE**

Write the converses of the following conditionals and determine the truth value of each 1) If two lines are both vertical, then they are parallel 2) If a number is not divisible by 10, then it is not divisible by 5 3) If the measure of an angle is between 0o and 90o, then the angle is acute

8
BICONDITIONAL – When the conditional and converse are both true, you can combine them using “if and only if” (iff) CONDITIONAL: If a polygon is a quadrilateral, then it has four sides. CONVERSE: If a polygon has four sides, then it is a quadrilateral BICONDITIONAL: A POLYGON IS A QUADRILATERAL IFF IT HAS FOUR SIDES.

9
**ALL GEOMETRY DEFINITIONS CAN BE WRITTEN AS BICONDITIONALS**

10
**Inverse-Negates the hypotheses and the conclusion of a conditional statement.**

Conditional: If you have a funny haircut, people will notice you. Inverse: If you do not have a funny haircut , people will not notice you.

11
**Conditional: If Monique finds a summer job, then she will buy a car.**

Contrapositive-interchanges and negates both the hypothesis and the conclusion of a conditional statement Conditional: If Monique finds a summer job, then she will buy a car. Find the Converse, Inverse and the Contrapositive statements. Converse: If Monique buys a car, then she will find a summer job. Inverse: If Monique does not find a summer job, then she will not buy a car. Contrapositive: If Monique does not buy a car, then she will not find a summer job.

12
**PRACTICE 1) If <A is a right angle then A B C**

Write the conditional, converse, biconditional, inverse and contrapositive for this picture.

13
**PRACTICE X 3) If M is the midpoint of DE then D E M**

Write the conditional, converse, and biconditional, inverse and contrapositive for this picture.

Similar presentations

Presentation is loading. Please wait....

OK

2.6 Proving Angles Congruent

2.6 Proving Angles Congruent

© 2018 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google

Ppt on product specification sheets Ppt on self help group in hindi Ppt on master production scheduling Ppt on role of construction industry in indian economy Project ppt on introduction to business finance Ppt on australian continent history Ppt on pricing policy pdf Ppt on social contract theory and declaration Ppt on natural resources of earth Ppt on 98 notified sections of companies act 2013