Transcript “if-then” form

Conditional Statements
A conditional statement is a statement that can
be written in “if-then” form.
The hypothesis of the statement is the phrase
immediately following the word “if”.
The conclusion is the phrase following “then”.
Example: If our team wins Friday night, then we
will be the state champions.
Hypothesis: our team wins Friday night
Conclusion: we will be the state champions
We use symbols to represent the parts of a
conditional statement. We use the letter p to
represent the hypothesis, and the letter q to
represent the conclusion. We may need more
letters if there are several statements to be
considered.
Using these symbols, we can write the following:
p→q which mean “if p then q” or “p implies q”
If points A, B, and C lie on line m, then they are
collinear.
Hypothesis:
Conclusion:
The Tigers will play in the tournament if they win
their next game.
p:
q:
An angle with measure greater than 90 is an
obtuse angle.
Hypothesis:
Conclusion:
Now we rewrite the statement in “if-then” form:
Perpendicular lines intersect.
Sometimes we must add information to put the
statement into true conditional format.
Now we rewrite the statement in “if-then” form:
Identify the hypothesis and conclusion of the
following statements.
1) If a polygon has 6 sides, then it is a hexagon.
2) If you are a baby, then you will cry.
3) To find the distance between two points, you can
use the Distance Formula.
Identify the hypothesis and conclusion of the
following statement. Then write the statement
in the if-then form.
1) Distance is positive.
2) A five-sided polygon is a pentagon.
Identify the hypothesis and conclusion of each
statement. Then write each statement in if-then form.
a. A polygon with 8 sides is an octagon.
b. An angle that measures 45º is an acute angle.
Other Forms of Conditionals
Converse: Reverse the hypothesis and conclusion
in a conditional statement. For example:
Conditional: If it rained today, then my yard got wet.
Converse: If my yard got wet, then it rained today.
In symbols, if the conditional is p→q, then the
converse is q→p.
Notice that when a conditional is true, the
converse may not be true. In geometry, we will
always be striving to examine statements to
determine if they are true and if their converse is
also true.
1) Write the converse, of the statement All squares
are rectangles.
2) Determine whether each statement is true or false.
If a statement is false, give a counterexample.
Conditional:
Converse:
1) Write the converse of the statement The sum of
the measures of two complementary angles is 90.
2) Determine whether each statement is true or false.
If a statement is false, give a counterexample.
1) Write the converse of the statement Linear pairs of
angles are supplementary.
2) Determine whether each statement is true or false.
If a statement is false, give a counterexample.