Download If-Then Statements

DO NOW…
1.
Compare/Contrast the vocabulary words
CONJUNCTION and DISJUNCTION.
2.
Create your own example to illustrate each
HONORS GEOMETRY
2.1 INDUCTIVE REASONING & PROOF
2.2 LOGIC
2.3 CONDITIONAL STATEMENTS
VOCABULARY

Conditional statement

if-then statements

hypothesis

conclusion

converse

inverse

contrapositive
IF-THEN STATEMENTS
 Identify
the HYPOTHESIS and CONCLUSION.
If you attend CDHS, then your mascot is the Ram.
(The hypothesis/conclusion DOES NOT include the IF and THEN)
IF-THEN STATEMENTS
 Identify
the HYPOTHESIS and CONCLUSION.
If you attend CDHS, then your mascot is the Ram.
H: you attend CDHS
C: your mascot is the Ram
(The hypothesis/conclusion DOES NOT include the IF and THEN)
CHANGE THE STATEMENT TO IF-THEN FORM, THEN
IDENTIFY THE HYPOTHESIS AND CONCLUSION.
The intersection of two planes is a line.
CHANGE THE STATEMENT TO IF-THEN FORM, THEN
IDENTIFY THE HYPOTHESIS AND CONCLUSION.
The intersection of two planes is a line.
If two planes intersect, then a line is formed.
CHANGE THE STATEMENT TO IF-THEN FORM, THEN
IDENTIFY THE HYPOTHESIS AND CONCLUSION.
The intersection of two planes is a line.
If two planes intersect, then a line is formed.
H: two planes intersect
C: a line is formed
NOTATION
The sum of the measures of two complimentary angles is 90˚.

Conditional:
𝒑→𝒒
NOTATION
The sum of the measures of two complimentary angles is 90˚.
Conditional: 𝒑 → 𝒒
 If two angles are complementary, then the sum of their measures is 90˚.

NOTATION
The sum of the measures of two complimentary angles is 90˚.
Conditional: 𝒑 → 𝒒
 If two angles are complementary, then the sum of their measures is 90˚.


Inverse: ~𝒑 → ~𝒒
NOTATION
The sum of the measures of two complimentary angles is 90˚.
Conditional: 𝒑 → 𝒒
 If two angles are complementary, then the sum of their measures is 90˚.

Inverse: ~𝒑 → ~𝒒
 If two angles are not complementary, then the sum of their measures is
not 90˚.

NOTATION
The sum of the measures of two complimentary angles is 90˚.
Conditional: 𝒑 → 𝒒
 If two angles are complementary, then the sum of their measures is 90˚.

Inverse: ~𝒑 → ~𝒒
 If two angles are not complementary, then the sum of their measures is
not 90˚.



Converse: 𝒒 → 𝒑
NOTATION
The sum of the measures of two complimentary angles is 90˚.
Conditional: 𝒑 → 𝒒
 If two angles are complementary, then the sum of their measures is 90˚.

Inverse: ~𝒑 → ~𝒒
 If two angles are not complementary, then the sum of their measures is
not 90˚.

Converse: 𝒒 → 𝒑
 If the sum of the measures of two angles is 90˚, then they are
complementary.

NOTATION
The sum of the measures of two complimentary angles is 90˚.




Conditional: 𝒑 → 𝒒
If two angles are complementary, then the sum of their measures is 90˚.
Inverse: ~𝒑 → ~𝒒
If two angles are not complementary, then the sum of their measures is not 90˚.

Converse: 𝒒 → 𝒑
If the sum of the measures of two angles is 90˚, then they are complementary.

Contrapositive: ~𝒒 → ~𝒑

NOTATION
The sum of the measures of two complimentary angles is 90˚.








Conditional: 𝒑 → 𝒒
If two angles are complementary, then the sum of their measures is 90˚.
Inverse: ~𝒑 → ~𝒒
If two angles are not complementary, then the sum of their measures is not 90˚.
Converse: 𝒒 → 𝒑
If the sum of the measures of two angles is 90˚, then they are complementary.
Contrapositive: ~𝒒 → ~𝒑
If the sum of the measures of two angles is not 90˚, then they are not
complementary.
YOUR TURN...WRITE THE INVERSE,
CONVERSE, AND CONTRAPOSITIVE
 Conditional:
𝒑→𝒒
If it is down-pouring rain, then it is cloudy outside.
 Inverse:
~𝒑 → ~𝒒
 Converse:
𝒒→𝒑
 Contrapositive:
~𝒒 → ~𝒑
YOUR TURN...WRITE THE INVERSE,
CONVERSE, AND CONTRAPOSITIVE
 Conditional:
𝒑→𝒒
If it is down-pouring rain, then it is cloudy outside.
 Inverse:
~𝒑 → ~𝒒
If it is not down-pouring rain, then it is not cloudy outside.
 Converse:
𝒒→𝒑
If it is cloudy outside, then it is down-pouring rain.
 Contrapositive:
~𝒒 → ~𝒑
If it is not cloudy outside, then it is not down-pouring rain.
WRITE THE INVERSE, CONVERSE, AND
CONTRAPOSITIVE FOR THE STATEMENT BELOW:
“Those who do not remember the past are condemned to
repeat it” – George Santayana
WRITE THE INVERSE, CONVERSE, AND
CONTRAPOSITIVE FOR THE STATEMENT BELOW:
“Those who do not remember the past are condemned to
repeat it” – George Santayana
 Conditional: 𝒑 → 𝒒
 If you do not remember the past, then you are condemned to repeat
it.
WRITE THE INVERSE, CONVERSE, AND
CONTRAPOSITIVE FOR THE STATEMENT BELOW:
“Those who do not remember the past are condemned to
repeat it” – George Santayana
 Conditional: 𝒑 → 𝒒
 If you do not remember the past, then you are condemned to repeat
it.
Inverse: ~𝒑 → ~𝒒
 If you do remember the past, then you are not condemned to repeat
it.

WRITE THE INVERSE, CONVERSE, AND
CONTRAPOSITIVE FOR THE STATEMENT BELOW:
“Those who do not remember the past are condemned to
repeat it” – George Santayana
 Conditional: 𝒑 → 𝒒
 If you do not remember the past, then you are condemned to repeat it.




Inverse: ~𝒑 → ~𝒒
If you do remember the past, then you are not condemned to repeat it.
Converse: 𝒒 → 𝒑
If you are condemned to repeat the past, then you do not remember the
past.
WRITE THE INVERSE, CONVERSE, AND
CONTRAPOSITIVE FOR THE STATEMENT BELOW:
“Those who do not remember the past are condemned to repeat it” –
George Santayana
 Conditional: 𝒑 → 𝒒
 If you do not remember the past, then you are condemned to repeat it.






Inverse: ~𝒑 → ~𝒒
If you do remember the past, then you are not condemned to repeat it.
Converse: 𝒒 → 𝒑
If you are condemned to repeat the past, then you do not remember the past.
Contrapositive: ~𝒒 → ~𝒑
If you are not condemned to repeat the past, then you do remember the past.
WRITE THE INVERSE, CONVERSE, AND
CONTRAPOSITIVE FOR THE STATEMENT BELOW:
“Those who do not remember the past are condemned to repeat it” –
George Santayana
 Conditional: 𝒑 → 𝒒
 If you do not remember the past, then you are condemned to repeat it.






Inverse: ~𝒑 → ~𝒒
If you do remember the past, then you are not condemned to repeat it.
Converse: 𝒒 → 𝒑
If you are condemned to repeat the past, then you do not remember the past.
Contrapositive: ~𝒒 → ~𝒑
If you are not condemned to repeat the past, then you do remember the past.