Transcript 2.2 Definition and Biconditional Statements

2.2 Definition and
Biconditional Statements
Use definitions and biconditional
statements
Definition is used to describe
In Geometry definitions describe and
carry information.
Definition of perpendicular lines : lines
that form right angle.
Here we know that perpendicular lines
make right angles
 Definition of a perpendicular line to a
plane : A line which is perpendicular
to every line on the plane at the point
of intersection.
Classify the angles
B
A
X
D
AXB
C
AXC
AXD
How to Write Perpendicular Lines
AC
BD
This means that Line AC is
perpendicular to line BD
An upside down T means perpendicular
Conditional Statement and its
Converse
A conditional statement and its converse
can be combined to make a
Biconditional statement
Biconditional statement can also be true
or false
If it is a line, then it contains two points
If it contains two points, then it is a line
As a biconditional statement
It is a line if and only if it contains at
least two points
if and only if as often written as iff
Write as two statements
Two angles are complementary if and
only if their sum is 90 degrees.
Write as two statements
Two angles are complementary if and only
if their sum is 90 degrees.
If two angles are complementary, then
their sum is 90 degrees.
If the sum of two angles is 90 degrees,
then the two angles are complementary
Is this biconditional statement true?
x2 ≤ 49 if and only if x ≤ 7
Homework
Page 82-83
#13 – 31
Homework
Page 83 – 84
# 32 – 44, 50, 59 - 68