Transcript Recognizing Conditional Statements

Conditional Statements
Goals
•Recognize a conditional statement
•Write the converse, inverse, and
conditional statement
Recognizing Conditional Statements
Conditional Statements
If-Then Statements
If a number is divisible by both 2 and 3 then it is divisible by 6.
HYPOTHESIS
CONCLUSION
If a polygon has four sides then it is a quadrilateral.
If a number greater than two is even, then it is not prime.
Recognizing Conditional Statements
Conditional statements can be True or
False
• To show a conditional statement is true, you
must present an argument to show true in all
cases.
• To show conditional statement is false, you
only have to have a single counterexample.
Recognizing Conditional Statements
Example:
Write a counterexample:
If a number is odd, then it is divisible by 3
Recognizing Conditional Statements
Example 1
State the hypothesis and
conclusion for each statement.
IF two angles are supplementary, THEN the
sum of their angles is 180 degrees.
IF you are 5 feet tall, THEN are also 60 inches
tall.
Recognizing Conditional Statements
Example 2
State the hypothesis and
conclusion for each statement.
IF two angles are adjacent, THEN they have
a common vertex.
Recognizing Conditional Statements
Example 2
Rewrite in if-then form
All monkeys have tails.
If animal is a monkey, then the animal has a
tail.
Vertical angles are congruent.
If two angles are vertical, then they are
congruent.
Recognizing Conditional Statements
Example 2
Rewrite in if-then form
Supplementary angles have measures
whose sum is 180°.
Recognizing Conditional Statements
The CONVERSE of a conditional statement
is formed by interchanging the hypothesis
and conclusion.
conditional statement
If x – y is positive then x > y .
converse
If x > y then x – y is positive.
Recognizing Conditional Statements
1. IF two angles are adjacent, THEN they have a
common vertex.
CONVERSE - IF two angles have a common vertex,
THEN they are adjacent.
2. IF two angles are supplementary, THEN the sum
of their angles is 180 degrees.
CONVERSE - IF two angles have a sum of 180
degrees, THEN they are supplementary.
3. IF you are 5 feet tall, THEN are also 60 inches tall.
CONVERSE - IF you are 60 inches tall, THEN are
also 5 feet tall.
Recognizing Conditional Statements
The denial of a statement is called a NEGATION.
RST is an obtuse angle.
Intersecting lines are coplanar.
If we take a test today we do not have
homework.
Recognizing Conditional Statements
Given a conditional statement, its INVERSE can
be formed by negating both the hypothesis and
conclusion.
The inverse of a true statement is not necessarily true.
EXAMPLE
Conditional statement: If the angle is 75 degrees, then it
is acute.
Inverse: If the angle is not 75 degrees, then it is not
acute.
Recognizing Conditional Statements
Example 3
Find the inverse of the following statement. Is it True
or False
If you have vertical angles, then they
are congruent.
Recognizing Conditional Statements
CONTRAPOSITIVE: Formed by negating the
hypothesis and conclusion of the converse of
the given conditional.
When forming a contrapositive of a conditional it may be
easier to write the converse first – then negate each part.
Example:
Statement: If the angle is 75 degrees then it is acute .
Recognizing Conditional Statements
Example 5:
Write the contrapositive of the conditional statement
If two angles are vertical, then they are congruent.
Recognizing Conditional Statements
Original
If mA = 30°, then  A is acute.
Inverse
If mA  30°, then  A is not acute.
Converse
If  A is acute then mA = 30°.
Contrapositive If  A is not acute then mA  30°.
.
Biconditional Statements
• Biconditional statement is when the
conditional statement and converse are both
true. It can be written as an “if and only if”
statement.
• An angle is called a right angle if and only
if it measures 90 degrees.
Write the converse, inverse, contrapositive, and
biconditional statement for the following conditional
statement.
If a triangle is isosceles, then it has two
congruent sides.