Download Conditional Statement

2-2 Conditional Statements
Conditional Statement—is a statement that can be written in the form of “if p, then q.”
In symbol, it is p  q
Hypothesis—the “p” part of a conditional statement. It is the part of the statement following
the word “if.”
Conclusion—the “q” part of a conditional statement. It is the part of the statement following
the word “then.”
If two lines interest, then they intersect in exactly one point.
A rhombus is a square, if it has 4 right angles.
Writing a statement as a conditional statement: To do this, decide which part of statement
depends upon the other.
EX: Cars with underinflated tires waste gasoline.
If a car has underinflated tires, then it wastes gasoline.
Ex: An obtuse triangle has exactly one obtuse angle.
If ________________________________, then_______________________________
Counterexample-- An example that proves that a conjecture or statement is false. You only
need one counterexample to prove the statement is false.
If the sidewalk is wet, then it is raining. False—could be a sprinkler, snowing, etc
If the diagonals are congruent, then the quadrilateral is a rectangle.
Converse—The converse of the conditional statement interchanges (switches) the hypothesis
and the conclusion. “If p, then q” now becomes “If q, then p”
Example:
Statement:
If a quadrilateral is a trapezoid, then it has one pair of parallel sides.
Converse:
If it has one pair of parallel sides, then a quadrilateral is a trapezoid.
Statement: If I play boys high school soccer in Michigan, then I play in the fall season.
Converse:
Statement: If a quadrilateral is a rhombus, then it has perpendicular diagonals.
Converse:
Statement: If two lines are parallel, then they do not intersect.
Converse:
Do not assume that the converse of statement or theorem is true just because the original
statement is true. The converse of a theorem must be proved true!!
Related Conditionals
Negation—is the opposite. “p” becomes “not p” or ~p .
Statement: I go to Lake Shore High School.
Negation: I do NOT go to Lake Shore High School.
Statement: I am not 16 years old.
Negation:
Conditional Statement—“If p, then q” p  q
Inverse: “If NOT p, then NOT q.” ~ p  ~q
Converse: Íf q, then p.
qp
Contrapositive: “If NOT q, then NOT p” ~ q  ~ p
Statement: A square is a rhombus
Conditional—If a quadrilateral is a square, then it is a rhombus.
True
Inverse—If a quadrilateral is not a square, then it is not a rhombus.
False _________________________________________
Converse—If a quadrilateral is a rhombus, then it is a square.
False ___________________________________________
Contrapositive—If a quadrilateral is not a rhombus, then it is not a square.
True
Statement: Two angles that add to 180° are supplementary.
Conditional: If two angles are supplementary, then they add to 180°.
Inverse:
Converse:
Contrapositive:
Writing a conditional statement from a Venn Diagram:
The inner oval represents the hypothesis and the outer oval represents the conclusion.
If a polygon is a square, then it is a
parallelogram.
Parallelograms
Square
s
Draw a Venn diagram for this conditional statement:
If an angle measures 100°, then it is obtuse.