Transcript “if” “p” - msmatthewsschs

2.2 – Analyze Conditional Statements
Conditional
Statement
Hypothesis
Conclusion
Logical statement written in
if-then form. If p, then q.
pq
Statement following the “if”
“p” part
Statement following the “then”
“q” part
True Statement
Assuming “p” is true, the “q”
HAS to happen
Assuming “p” is true, the “q”
might not happen. You only
False Statement
need ONE example to prove a
statement false.
One example that proves a
Counterexample statement is false. When p is
true, but q is false.
Converse
Inverse
Flip the hypothesis and
conclusion
If p, then q becomes If q, then p
qp
Negate the hypothesis and
conclusion
If p, then q becomes If not p,
then not q ~p  ~q
Contrapositive
Negate the hypothesis and
conclusion of the converse
If p, then q becomes If not q,
then not p ~q  ~p
Equivalent to the original
statement.
Original and converse of a
statement are true.
Biconditional
statement
p if and only if q
p iff q
p  q AND q  p
pq
Perpendicular Lines: Two lines that intersect
to form four right angles
1. Rewrite the definition of perpendicular lines in if-then
form.
If two lines are perpendicular, then
they intersect to form four right angles.
Decide whether the statement is true or false. If false,
provide a counterexample.
If A is obtuse, then it measures 155°
False, A is obtuse and measures 100°
State the hypothesis, conclusion, and converse.
Determine if the converse is true.
If you are a football player, then you are an athlete.
hypothesis
conclusion
Converse:
If you are a athlete, then you are a football player.
False, you can be an athlete in cross-country.
State the hypothesis, conclusion, and converse.
Determine if the converse is true.
If x = 3, then x2 = 9.
hypothesis
conclusion
Converse: If x2 = 9, then x = 3.
False, x2 = 9 and x = -3
4. Rewrite the statement in if-then form. Then write the
converse, the inverse, and the contrapositive.
A car runs when there is gas in the tank.
If-then:
If a car is running, then there is gas in the tank.
Converse: If there is gas in the tank, then the car is
running.
Inverse:
If the car isn’t running, then there isn’t gas in
the tank.
Contra:
If there isn’t gas in the tank, then the car isn’t
running.
4. Rewrite the statement in if-then form. Then write the
converse, the inverse, and the contrapositive.
All triangles have three sides.
If-then:
If a polygon is a triangle, then it has 3 sides.
Converse: If a polygon has 3 sides, then it is a triangle.
Inverse:
If a polygon isn’t a triangle, then it doesn’t
have 3 sides.
Contra:
If a polygon doesn’t have 3 sides, then it isn’t a
triangle.
5. Determine if the if-then statement is true or
false. If false, provide a counterexample.
If you drive a mustang, then it is red.
False, You drive a mustang that is black.
5. Determine if the if-then statement is true or
false. If false, provide a counterexample.
If T is between S and R, then ST + TR = TS.
S
T
R
False, T is between S and R, then ST + TR = SR
5. Determine if the if-then statement is true or
false. If false, provide a counterexample.
If m2 = 90°, then it is a right angle.
True
6. Decide whether each statement about the diagram
is true. Explain your answer.
mAEB = 90°
True,
it is a right angle
6. Decide whether each statement about the diagram
is true. Explain your answer.
AE + EC = 180°
False,
Segments aren’t
measured in degrees!
7. Rewrite the definition as a biconditional statement.
Two angles are complementary angles if the sum of
their measures is 90°
Two angles are complementary angles iff their sum
measures 90°
7. Rewrite the definition as a biconditional statement.
The midpoint of a segment is a point that divides the
segment into two congruent segments.
A point is the midpoint of a segment iff it is a point
that divides the segment into two congruent segments.
THE FIRE-FISH STORY
“If there is a fire, then a fish dies”
You are to write a creative story consisting entirely of conditional
statements. The first statement should be of the form: “If there
is a fire, then A.” The second statement should be of the
form: “If A, then B.” The hypothesis of each statement must be
the conclusion of the previous statement. The story must be out
of at least 5 conditional statements, ending with “If D, then a
fish dies.”
If there is a fire, then ___________________________________.
If ________________, then …………………………………
If …………………………., then ***************************************.
If
*******************************,
then xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx.
If xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx, then a fish dies.
HW Problem
2.2
82-85
1-15 odd, 16-18, 19-27 odd
# 19
Ans:
An angle measures between 90° and 180° iff it is
obtuse