Cornell Notes Template Geometry 1 Unit 2: Reasoning And Proof Page 6
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16Geometry 1
Unit 2: Reasoning and Proof
2.2- Biconditional Statements
Can be rewritten with “____ _______ _________ ______”
Only occurs when the statement and the converse of the
Biconditional Statement
statement are both _________.
A biconditional can be split into a conditional and its converse.
An angle is right if and only if its measure is 90º
A number is even if and only if it is divisible by two.
Example 1
Determine whether the
A point on a segment is the midpoint of the segment if
biconditional is true.
and only if it bisects the segment.
You attend school if and only if it is a weekday.
Two lines are perpendicular if they intersect to form a
Perpendicular Lines
______________ angle.
A line perpendicular to a
A line that intersects the plane in a point and is perpendicular
plane
to every line in the plane that intersects it
The symbol
is read as, “is perpendicular to.”
Write the definition of perpendicular as a biconditional.
Example 2
Give a counterexample that demonstrates that the converse is
false.
If two lines are perpendicular, then they intersect.
Example 3
The following statement is true. Write the converse and
decide if it is true or false. If the converse is true, combine it
with its original to form a biconditional.
2
Example 4
If x
= 4, then x = 2 or x = -2
2
Consider the statement:
x
< 49 if and only if x < 7.
Is this a biconditional?
Example 5
Is the statement true?
5
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