RGeom2.2_CondStatements.notebook
September 27, 2016
Homework ­ pg. 75: 3, 5­8, 14­17, 19, 32 pg. 82: 3, 4, 7
0.625
divide by 2
Rewrite in if-then form
If two angles are complementary, then they add to 90.
If two angles add to 90, then they are complementary.
1
RGeom2.2_CondStatements.notebook
September 27, 2016
2.1 Warm-up
1.
2.
3.
2
RGeom2.2_CondStatements.notebook
September 27, 2016
2.2 Analyze Conditional Statements
Example:
Conditional
Statement
A logical statement that has a
hypothesis and a conclusion.
Converse
When the original hypothesis and
conclusion are switched.
Inverse
The negative form of the original
conditional statement.
Conditional Statement
If a dog is a Great Dane, then it is large.
When the original hypothesis and
Contrapositive conclusion are switched AND
made negative.
Just because a statement is written doesn't make it true!
We must check for true or false statements.
3
RGeom2.2_CondStatements.notebook
September 27, 2016
Write the converse, the inverse, and the contrapositive
of the conditional statement. Tell whether each
statement is true or false.
Soccer players are athletes.
Conditional Statement
If a person plays soccer then he/she is an athlete
Converse
If a person is an athlete then he/she plays soccer
Inverse
If a person does not play soccer then he/she is not an athlete
Contrapositive
If a person is not an athlete then he/she does not play soccer
4
RGeom2.2_CondStatements.notebook
September 27, 2016
Write the converse, the inverse, and the contrapositive
of the conditional statement. Tell whether each
statement is true or false.
All 90° angles are right angles.
Conditional Statement
If an angle measures 90 degrees then it is a right angle
Converse
If an angle is a right angle the it measures 90 degrees
Inverse
If an angle is not 90 degrees then it is not a right angle
Contrapositive
If an angle is not a right then it is not 90 degrees
5
RGeom2.2_CondStatements.notebook
September 27, 2016
Biconditional Statement: A statement that combines a conditional
statement and its converse if both are true. Use the phrase "if and
only if".
An angle measures 90 degrees if and only if it is a right angle.
An angle is a right angle if and only if it measures 90 degrees.
6
RGeom2.2_CondStatements.notebook
September 27, 2016
Example 2:
____
Conditional: If today is Friday, then tomorrow is Saturday.
____
Converse:
If both are true, write as a biconditional statement
7
RGeom2.2_CondStatements.notebook
September 27, 2016
Rewrite the following as a biconditional statement:
A rhombus is a figure with four sides that are equal in length.
8
RGeom2.2_CondStatements.notebook
September 27, 2016
Homework
pg. 82: 8-10,12,13,19,25,33
9
RGeom2.2_CondStatements.notebook
September 27, 2016
Homework - pg. 82: 8-10,12,13,19,25,33
10