Download Objective # 26: Conditional and Converse Statements Material

Objective # 26:
Material:
Conditional and Converse Statements
page 208 to 212
Homework: worksheet
Conditional statement
is a statement made of two parts a hypothesis and a conclusion.
IF - THEN form of a Conditional statement:
When the statement is written in if-then form, the “if” part contains the
hypothesis and the “then” part contains the conclusion.
Converse of a Conditional statement
is the statement formed by switching the hypothesis and the
conclusion.
Example 1:
Conditional Statement:
If x = 2, then x is an even integer between 1 and 3.
Converse Statement:
If x is an even integer between 1 and 3, then x = 2.
IFF statement:
Example 2:
If both a statement and its converse are true then the if and then can be replaced by
iff written between the two parts of the statement. Iff means if and only if
In example 1, since both the statement and its converse are true. They can be written as:
x = 2 iff x is an even integer between 1 and 3.
Example 3:
Conditional Statement :
If you are in Advanced Math, then you know your logarithm rules.
Converse Statement:
If you know your logarithm rules, then you are in Advanced Math.
Caution!! Not all converses are necessarily true!! Example 2 illustrates this fact. There are plenty of
people who know their log rules but take regular math, calculus, etc. Therefore, these statements should
not be rewritten using an iff.
Conditional and Converse Statements
Worksheet
For each of the following conditional statements, state the converse statement. If both the conditional and
the converse statements are true, write an iff statement.
1. If she is inside the house, then she cannot see the moon.
2. If it is blue, then it is not green.
3. If two segments have the same measure, then they are congruent.
4. If two lines are perpendicular, then they intersect at right angles.
5. If all three sides of a triangle are equal then, the triangle is equilateral.
6. If two triangles are congruent, then they are similar.
7. If a polygon has four sides, then it is a square.
8. If Alice’s daughter is married, then Alice is a parent.
9. If x = 12 then x <20.
10. If three points are noncollinear, then they form a triangle.
11. If a triangle has two congruent sides, then it also has two congruent angles.
12. If a quadrilateral is a square, then it has four congruent sides.
13. If two lines are parallel, then they never meet.