Download Conditional Statement

Geometry
2.2 Conditional Statements
Name: ____________________________
A ___________________________________ is a logical statement that has two parts.
1. __________________________________
2. __________________________________
Ex. If it is raining, then there are clouds in the sky.
Rewrite the following statements as a conditional statement.
a) Two angles are supplementary if they are a linear pair.
b) All 90° angles are right angles.
Negation: The opposite of the original statement
Ex.
Statement: Geometry is fun
Negation: Geometry is not fun
Conditional Statement
Conditional Statements can be either
__________________ or __________________.


To show true, you must prove that the
conclusion is true every time the
hypothesis is true.
To show false, you only need to give
___________ counterexample.
Inverse
 Negate the ___________________________
statement.
Converse
 Exchange the _______________________
with the _____________________
 Switch the parts after the ________ and
______________.
Contrapositive
 Negate the ___________________________
 Make sure to negate both parts!
 Make sure to negate both parts!
Complete the chart:
Conditional Statement: If 𝑚 < 𝐴 = 100°, then < 𝐴 is obtuse
Converse:
Inverse:
Contrapositive:
Equivalent Statements:
 A conditional statement and its ________________________ are either both true or both false.

The converse and the __________________ are also either both true or both false.

Two statements that are either both true or both false are known as _____________________.
Write each type below and determine whether each statement is true or false.
Statement: Soccer players are athletes.
Conditional Statement:
Converse:
Inverse:
Contrapositive:
Definitions: Can be written as a _______________________________ statement
or as its
________________________________
Perpendicular Lines- If two lines intersect to form a _____________ angle, then they are
perpendicular lines.
l
Converse:
m
Notation:
Decide whether each statement about the diagram is true. Explain.
⃡ ⊥ 𝐵𝐷
⃡
𝑎) 𝐴𝐶
B
A
C
E
D
b) < 𝐴𝐸𝐵 and < 𝐶𝐸𝐵 are a linear pair
c) 𝐸𝐴 and 𝐸𝐵 are opposite rays.
Biconditional Statements
 When a conditional statement and its converse are both true, you can write one single
statement called a _______________________ statement.
 They contain the phrase: ______________________________
1. Perpendicular Lines:
If two lines intersect to form a right angle, then they are perpendicular lines.
Converse:
Biconditional:
2. Equilateral Triangles:
If the sides of a triangle are all the same length, then the triangle is equilateral.
Converse:
Biconditional: