2.1 conditional statements - montgomery county public schools
TRANSCRIPT
2.1 Conditional Statements
Mr. Peebles
Geometry
Spring 2013
Standards/Objectives:
Daily Learning Target (DLT)
Tuesday March 19, 2013
“I can recognize and analyze a conditional
statement and write postulates about
points, lines, and planes using
conditional statements.”
Geometry Bell Ringer: Simplify
8 ft__ =
27 in
Geometry Bell Ringer: Simplify
8 ft__ =
27 in
96 in =
27 in
32 in
9 in
What’s a Conditional Statement
A logical statement with 2 parts
2 parts are called the hypothesis &
conclusion
Can be written in “if-then” form; such as,
“If…, then…”
Conditional Statement (p q)
Hypothesis is the part after the word “If”
Conclusion is the part after the word
“then”
Ex: Underline the hypothesis &
circle the conclusion.
If you are a brunette, then you have brown hair.
hypothesis conclusion
Ex: Rewrite the statement in “if-then” form
1. Vertical angles are congruent.
If there are 2 vertical angles, then they are
congruent.
If 2 angles are vertical, then they are
congruent.
Ex: Rewrite the statement in “if-then” form
2. An object weighs one ton if it weighs
2000 lbs.
If an object weighs 2000 lbs, then it weighs
one ton.
Counterexample
Used to show a conditional statement is
false.
It must keep the hypothesis true, but
the conclusion false!
Ex: Find a counterexample to prove the
statement is false.
If x2=81, then x must equal 9.
Ex: Find a counterexample to prove the
statement is false.
If x2=81, then x must equal 9.
counterexample: x could be -9
because (-9)2=81, but x≠9.
Ex: Find a counterexample to prove the
statement is false.
If the light is green, then I can drive
through the intersection.
Ex: Find a counterexample to prove the
statement is false.
If the light is green, then I can drive
through the intersection.
Counterexample: Emergency Vehicles.
Converse (q p)
Switch the hypothesis & conclusion parts
of a conditional statement.
Ex: Write the converse of “If you are a
brunette, then you have brown hair.”
If you have brown hair, then you are a
brunette.
Inverse (~p ~q)
Negate the hypothesis & conclusion of a
conditional statement.
Ex: Write the inverse of “If you are a
brunette, then you have brown hair.”
If you are not a brunette, then you do
not have brown hair.
Contrapositive (~q ~p)
Negate, then switch the hypothesis &
conclusion of a conditional statement.
Ex: Write the contrapositive of “If you
are a brunette, then you have brown
hair.”
If you do not have brown hair, then
you are not a brunette.
The original conditional statement &
its contrapositive will always have
the same meaning.
The converse & inverse of a
conditional statement will always
have the same meaning.
Reminders:
IF-THEN Statement Example Pack
Write the following statements in IF-THEN
form from the given statement:
A right angle is 90 degrees.
1. Conditional: (p q)
2. Inverse: (~p ~q)
3. Converse: (q p)
4. Contrapositive: (~q ~p)
IF-THEN Statement Example Pack
Write the following statements in IF-THEN
form from the given statement:
A right angle is 90 degrees. 1. Conditional: (p q)
If it’s a right angle, then it’s 90 degrees.
2. Inverse: (~p ~q)
If it’s NOT a right angle, then it’s NOT 90 degrees.
3. Converse: (q p)
If it’s 90 degrees, then it’s a right angle.
4. Contrapositive: (~q ~p)
If it’s NOT 90 degrees, then it’s NOT a right angle.
IF-THEN Statement Example Pack
Write the following statements in IF-THEN
form from the given statement:
Good grades helps to get a Kentucky
Driver’s License.
1. Conditional: (p q)
2. Inverse: (~p ~q)
3. Converse: (q p)
4. Contrapositive: (~q ~p)
IF-THEN Statement Example Pack
Write the following statements in IF-THEN
form from the given statement: Good grades helps to get a Kentucky Driver’s License. 1. Conditional: (p q)
If I get good grades, then I can get a Kentucky Driver’s License.
2. Inverse: (~p ~q)
If I DON’T get good grades, then I CAN’T get a Kentucky Driver’s License.
3. Converse: (q p)
If I can get a Kentucky Driver’s License, then I can get good grades.
4. Contrapositive: (~q ~p)
If I CANNOT get a Kentucky Driver’s License, then I CANNOT get good
grades.
Assignment:
Pp. 83-86
(1-17 Odds, 31, 37, 39, 54-58, 64-66)
Closure: Whiteboards
In any IF-THEN statement, what part of
the statement is the hypothesis and what
part of the statement is the conclusion?
Closure: Whiteboards
In any IF-THEN statement, what part of
the statement is the hypothesis and what
part of the statement is the conclusion?
IF - Hypothesis
THEN - Conclusion