1) Conditional statements relate two parts - a hypothesis (if part) and a conclusion (then part). If the hypothesis is true, then the conclusion must be true as well. 2) The converse of a conditional statement switches the hypothesis and conclusion. The inverse negates both parts. The contrapositive obtains the inverse and then switches parts. 3) A biconditional statement uses "if and only if" to join a conditional statement with its converse when both are true. This creates a single statement expressing their relationship.

1. 7.1 CONDITIONAL
AND BICONDITIONAL
STATEMENTS
BY: JAY BASILGO
MARC OVILLE
DANNAH PAQUIBOT

2. CONDITIONAL STATEMENTS
EXAMPLE:
“If two distinct lines intersect,
then they intersect at exactly one
point.”

3. CONDITIONAL STATEMENTS
• If – then statements
•Consists of two parts:
- if , hypothesis
- then, conclusion

4. MORE EXAMPLES
•If two points lie in a plane, then the line
containing them lies in the plane.
Hypothesis: Two points lie in a plane.
Conclusion: The line containing them
lies in the plane.

5. MORE EXAMPLES
•If 2(x+5) = 12, then X = 1.
Hypothesis:
Conclusion:

6. MORE EXAMPLES
•A quadrilateral is a polygon.
•A prime number has 1 and itself as
factors.
•A square is a rectangle.

7. THE CONVERSE, INVERSE, AND
CONTRAPOSITIVE OF A CONDITIONAL
STATEMENT
It is said that if a statement is true, its
contrapositive is also true.
Moreover, if the converse is true, its inverse is also
true.
Consider the statement: if p, then q
i. Converse: If q, then p.
ii. Inverse: If not p, then not q.

8. CONVERSE
•To write the converse of a conditional
statement, simply interchange the hypothesis
and the conclusion. That is, the then part
becomes the if part.
•Note that converse of a conditional statement is
not always a true statement.

9. EXAMPLE
•a. If m<A= 9, then m<A is a Rigth angle.
Converse: If m<A is a right angle, then m<A = 90

10. EXAMPLE
•B. The intersection of two distinct planes is a
line.
If-then: If two distinct planes intersect, then their
intersection is a line.
Converse: If the intersection of two figures is a line,
then the figure are two distinct planes.

11. INVERSE
•To write the inverse of a conditional
statement, simply negate both the
hypothesis and conclusion.

12. EXAMPLE
• If m<A<90, then <A is an acute angle.
INVERSE: If m<A is not 90, then <A is not an acute
angle.
• If two distinct lines intersect, then they intersect at
one point.
INVERSE: if two distinct lines do not intersect, then
they do not intersect at a point.

13. CONTRAPOSITIVE
•To form the contrapositive of a conditional
statement, first, get its inverse. Then,
interchange its hypothesis and conclusion.

14. EXAMPLE
a. If m<A +m<B= 90, then <A and <B are
complementary.
Inverse: if m<A + m<B is not equal to
90, then <A and <B are complementary.
Contrapositive: If <A and <B are not
complementary, then m<A + B is not equal to
90.

15. BICONDITIONAL STATEMENT
•If a conditional statement and its converse are
both true. Then they can be joined together
into a single statement called biconditional
statement. Then this is done by using the
words if and only if.

16. EXAMPLE
a.If a+7= 12, then a = 5.
Conditional statement: if a+7 = 12,
then a = 5
Converse statement : If a = 5, then a +
7 = 12
*Both the conditional statement and its converse
are true statements. Hence, the biconditional statement