Geometry Conditional Statements 1 Conditional Statement Definition A

  • Slides: 17
Download presentation
Geometry Conditional Statements 1

Geometry Conditional Statements 1

Conditional Statement Definition: A conditional statement is a statement that can be written in

Conditional Statement Definition: A conditional statement is a statement that can be written in if-then form. “If _______, then _______. ” Example: If your feet smell and your nose runs, then you're built upside down. Continued…… 2

Conditional Statement - continued Conditional Statements have two parts: The hypothesis is the part

Conditional Statement - continued Conditional Statements have two parts: The hypothesis is the part of a conditional statement that follows “if” (when written in if-then form. ) The hypothesis is the given information, or the condition. The conclusion is the part of an if-then statement that follows “then” (when written in if-then form. ) The conclusion is the result of the given information. 3

Writing Conditional Statements Conditional statements can be written in “if-then” form to emphasize which

Writing Conditional Statements Conditional statements can be written in “if-then” form to emphasize which part is the hypothesis and which is the conclusion. Hint: Turn the subject into the hypothesis. Example 1: Vertical angles are congruent. can be written as. . . Conditional Statement: If two angles are vertical, then they are congruent. Example 2: Seals swim. can be written as. . . Conditional Statement: If an animal is a seal, then it swims. 4

If …Then vs. Implies Another way of writing an if-then statement is using the

If …Then vs. Implies Another way of writing an if-then statement is using the word implies. If two angles are vertical, then they are congruent. Two angles are vertical implies they are congruent. 5

Conditional Statements can be true or false: l A conditional statement is false only

Conditional Statements can be true or false: l A conditional statement is false only when the hypothesis is true, but the conclusion is false. l. A counterexample is an example used to show that a statement is not always true and therefore false. Statement: If you live in Virginia, then you live in Richmond. Is there a counterexample? Yes !!! Counterexample: I live in Virginia, BUT I live in Glen Allen. Therefore ( ) the statement is false. 6

Symbolic Logic l Symbols can be used to modify or connect statements. l Symbols

Symbolic Logic l Symbols can be used to modify or connect statements. l Symbols for Hypothesis and Conclusion: Hypothesis is represented by “p”. Conclusion is represented by “q”. if p, then q or p implies q Continued…. . 7

Symbolic Logic - continued p q is used to represent if p, then q

Symbolic Logic - continued p q is used to represent if p, then q or p implies q Example: p: a number is prime q: a number has exactly two divisors p q: If a number is prime, then it has exactly two divisors. Continued…. . 8

Symbolic Logic - continued ~ is used to represent the word Example 1: p:

Symbolic Logic - continued ~ is used to represent the word Example 1: p: the angle is obtuse ~p: The angle is not obtuse Note: ~p means that the angle could be acute, right, or straight. Example 2: ~p: “not” p: I am not happy I am happy ~p took the “not” out- it would have been a double negative (not not) 9

Forms of Conditional Statements Converse: Switch the hypothesis and conclusion (q p) p q

Forms of Conditional Statements Converse: Switch the hypothesis and conclusion (q p) p q If two angles are vertical, then they are congruent. q p If two angles are congruent, then they are vertical. Continued…. . 10

Forms of Conditional Statements Inverse: State the opposite of both the hypothesis and conclusion.

Forms of Conditional Statements Inverse: State the opposite of both the hypothesis and conclusion. (~p ~q) p q : If two angles are vertical, then they are congruent. ~p ~q: If two angles are not vertical, then they are not congruent. 11

Forms of Conditional Statements Contrapositive: Switch the hypothesis and conclusion and state their opposites.

Forms of Conditional Statements Contrapositive: Switch the hypothesis and conclusion and state their opposites. (~q ~p) p q : If two angles are vertical, then they are congruent. ~q ~p: If two angles are not congruent, then they are not vertical. 12

Forms of Conditional Statements l Contrapositives are logically equivalent to the original conditional statement.

Forms of Conditional Statements l Contrapositives are logically equivalent to the original conditional statement. l If p q is true, then q p is true. l If p q is false, then q p is false. 13

Biconditional l When a conditional statement and its converse are both true, the two

Biconditional l When a conditional statement and its converse are both true, the two statements may be combined. l Use the phrase if and only if (sometimes abbreviated: iff) Statement: If an angle is right then it has a measure of 90. Converse: If an angle measures 90 , then it is a right angle. Biconditional: An angle is right if and only if it measures 90. 14

Biconditional cont… l l Notice that the words if and then are removed from

Biconditional cont… l l Notice that the words if and then are removed from the statement, and the words if and only if are placed in the middle of the statement. Conditional: If two angles are supplementary, then their sum is 180. Is this a true statement? 15

l Converse: If two angles have a sum of 180, then they are supplementary.

l Converse: If two angles have a sum of 180, then they are supplementary. Is this a true statement? l Biconditional Statement: Two angles are supplementary if and only if their sum is 180. 16

For each of the following, write the conditional, converse, inverse, and contrapositive. It is

For each of the following, write the conditional, converse, inverse, and contrapositive. It is time for dinner if it is 6 P. M. 2. There are 12 eggs if the carton is full. 3. A number is divisible by 6 if it is divisible by 2 and 3. 4. You go to the hockey game if you like hockey. If the conditional and converse of any of these are both true, write a biconditional. 1. 17

Conditional Statements Conditional Statements A CONDITIONAL STATEMENT isConditional Statements Conditional Statements A CONDITIONAL STATEMENT is
2 1 Conditional Statements Conditional Statement Conditional statement2 1 Conditional Statements Conditional Statement Conditional statement
Conditional Statements 1 Conditional Statement Definition A conditionalConditional Statements 1 Conditional Statement Definition A conditional
Nested conditional statements Nested conditional statements A conditionalNested conditional statements Nested conditional statements A conditional
CONDITIONAL STATEMENTS Section 2 3 Conditional Statements ConditionalCONDITIONAL STATEMENTS Section 2 3 Conditional Statements Conditional
Conditional Statements and Conditional Statements Biconditional Statements WarmConditional Statements and Conditional Statements Biconditional Statements Warm
Conditional Statements Conditional Statements Ifthen statements are calledConditional Statements Conditional Statements Ifthen statements are called
Lesson Conditional Statements Conditional Statement Defn A conditionalLesson Conditional Statements Conditional Statement Defn A conditional
Lesson Conditional Statements Conditional Statement Defn A conditionalLesson Conditional Statements Conditional Statement Defn A conditional
Conditional Statements Switch Statements Why another conditional statementConditional Statements Switch Statements Why another conditional statement
Geometry 2 1 Conditional Statements VOCAB Conditional StatementGeometry 2 1 Conditional Statements VOCAB Conditional Statement
Conditional Statements Geometry 2 1 Conditional Statement AnConditional Statements Geometry 2 1 Conditional Statement An
Conditional Statements Vocabulary Conditional Statement A logical statementConditional Statements Vocabulary Conditional Statement A logical statement
Related Conditionals Conditional Statements Conditional Statement A statementRelated Conditionals Conditional Statements Conditional Statement A statement
2 2 Conditional Statements Conditional Statement A statement2 2 Conditional Statements Conditional Statement A statement
2 2 Conditional Statements Conditional Statements Definition A2 2 Conditional Statements Conditional Statements Definition A