H ONORS G EOMETRY 2-1 I NDUCTIVE R EASONING & C ONJECTURE 2-2 L OGIC 2-3 C ONDITIONAL STATEMENTS.
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HONORS GEOMETRY 2-1 INDUCTIVE REASONING & CONJECTURE 2-2 LOGIC 2-3 CONDITIONAL STATEMENTS
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Transcript of H ONORS G EOMETRY 2-1 I NDUCTIVE R EASONING & C ONJECTURE 2-2 L OGIC 2-3 C ONDITIONAL STATEMENTS.
HONORS GEOMETRY
2-1 INDUCTIVE REASONING & CONJECTURE2-2 LOGIC
2-3 CONDITIONAL STATEMENTS
VOCABULARY
If-then Statements
Conditional Statements
Hypothesis
Conclusion
Converse
Inverse
Contrapositive
EX 1:
Change the conditional statement below to IF-THEN form then identify the HYPOTHESIS and CONCLUSION.
Studying results in good grades
EX 1:
Change the conditional statement below to IF-THEN form then identify the HYPOTHESIS and CONCLUSION.
Studying results in good grades
If you study, then you will make good grades.
H: you study C: you will make good gradesHypothesis/Conclusion
DOES NOT include theIf and Then
YOU TRY:
Change the statement below to IF-THEN form then identify the HYPOTHESIS and CONCLUSION
A polygon with six sides is a hexagon.
Hypothesis/Conclusion DOES NOT include the
If and Then
YOU TRY:
Change the statement below to IF-THEN form then identify the HYPOTHESIS and CONCLUSION
A polygon with six sides is a hexagon.
If a polygon has six sides, then it is a hexagon.
H: a polygon has six sides C: it is a hexagon Hypothesis/Conclusion
DOES NOT include theIf and Then
CHANGING A CONDITIONAL STATEMENT
The three most common ways to change a conditional statement are by taking its: Inverse, Converse, or Contrapositive.
In each case, either the hypothesis and the conclusion switch places, or a statement is replaced by its negation.
CHANGING A CONDITIONAL STATEMENT
The sum of the measures of two complimentary angles is 90˚.
Conditional:
Converse:
Inverse:
Contrapositive:
CHANGING A CONDITIONAL STATEMENT
The sum of the measures of two complimentary angles is 90˚.
Conditional: If two angles are complimentary, then the sum of the
measures of the two angles is 90°.
Converse:
Inverse:
Contrapositive:
CHANGING A CONDITIONAL STATEMENT
The sum of the measures of two complimentary angles is 90˚.
Conditional: If two angles are complimentary, then the sum of the
measures of the two angles is 90°.
Converse: If the sum of the measures of two angles is 90°, then the two
angles are complimentary.
Inverse:
Contrapositive:
CHANGING A CONDITIONAL STATEMENT
The sum of the measures of two complimentary angles is 90˚.
Conditional: If two angles are complimentary, then the sum of the measures of
the two angles is 90°.
Converse: If the sum of the measures of two angles is 90°, then the two
angles are complimentary.
Inverse: If two angles are not complimentary, then the sum of the measures
of the two angles is not 90°.
Contrapositive:
CHANGING A CONDITIONAL STATEMENT
The sum of the measures of two complimentary angles is 90˚.
Conditional: If two angles are complimentary, then the sum of the measures of the
two angles is 90°.
Converse: If the sum of the measures of two angles is 90°, then the two angles are
complimentary.
Inverse: If two angles are not complimentary, then the sum of the measures of the
two angles is not 90°.
Contrapositive: If the sum of the measures of two angles is not 90°, then the two angles
are not complimentary.
CHANGING A CONDITIONAL STATEMENT
STATE THE TRUTH VALUE OF EACH STATEMENT.
Conditional: If two angles are complimentary, then the sum of the measures of the
two angles is 90°.
Converse: If the sum of the measures of two angles is 90°, then the two angles
are complimentary.
Inverse: If two angles are not complimentary, then the sum of the measures of
the two angles is not 90°.
Contrapositive: If the sum of the measures of two angles is not 90°, then the two
angles are not complimentary.
CHANGING A CONDITIONAL STATEMENT
STATE THE TRUTH VALUE OF EACH STATEMENT.
Conditional: If two angles are complimentary, then the sum of the measures of the
two angles is 90°. TRUE
Converse: If the sum of the measures of two angles is 90°, then the two angles
are complimentary. TRUE
Inverse: If two angles are not complimentary, then the sum of the measures of
the two angles is not 90°. TRUE
Contrapositive: If the sum of the measures of two angles is not 90°, then the two
angles are not complimentary. TRUE
YOUR TURN. WRITE EACH STATEMENT AND STATE ITS TRUTH VALUE.
Conditional: If a polygon is a square, then it is a rectangle.
Converse:
Inverse:
Contrapositive:
YOUR TURN. WRITE EACH STATEMENT AND STATE ITS TRUTH VALUE.
Conditional: If a polygon is a square, then it is a rectangle. TRUE
Converse: If a polygon is a rectangle, then it is a square. FALSE
Inverse: If a polygon is not a square, then it is not a rectangle. FALSE
Contrapositive: If a polygon is not a rectangle, then it is not a square. TRUE
TICKET OUT THE DOOR:Write the If-Then Conditional, Converse, Inverse, and Contrapositive.
“Those who do not remember the past are condemned to repeat it.” – George Santayana
TICKET OUT THE DOOR:Write the If-Then Conditional, Converse, Inverse, and Contrapositive.
“Those who do not remember the past are condemned to repeat it” – George Santayana
Conditional: If you do not remember the past, then you are condemned to repeat it.
Converse: If you are condemned to repeat it, then you do not remember the past.
Inverse: If you do remember the past, then you are not condemned to repeat it. Contrapositive: If you are not condemned to repeat it, then you do remember the past.
