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Applied Geometry
Lesson 1-4
Conditional Statements &
Their Converses
Objective:
Learn to write statements in if-then form and write
the converses of the statements.
Conditional Statements
Conditional statement:
 A statement written in the form ifthen
If-then statement:
 A statement written in the form ifthen
Definitions
Hypothesis:
 The
part following the if in a
conditional statement.
Conclusion:
 The
part following the then in a
conditional statement.
Identify the Hypothesis
and Conclusion
If it is Saturday, then Elisa plays soccer.
H
C
H: it is Saturday
C: Elisa plays soccer
If two lines intersect, then their intersection
is a point.
H: two lines intersect
C: their intersection is a point
True or False
If it is the fourth of July, then it is a
holiday. True
If an animal lives in the water, then
it is a fish.
False, counterexample whales are not fish
Conditional Statements
3 ways of writing
If, then

If you are a member of Congress, then you are
a U.S. citizen.
(then), if

You are a U.S. citizen, if you are a member of
Congress.
Everyday

All members of Congress are U.S.
Write 2 other forms of the
statement.
If points are collinear, then they lie on the same
line
First identify the form of the original statement.
The form is in if, then form
So the forms we need are (then), if and everyday.
Points lie on the same line, if they are collinear.
(switch the subject since you can’t start a sentence with ‘they’.)
Points that lie on the same line are collinear.
Write 2 other forms
If three points are noncollinear,
then they determine a plane.
Three points determine a plane, if they
are noncollinear.
Three noncollinear points determine a plane.
Write 2 other forms
All collinear points lie on the same
line.
If points are collinear, then they lie on the
same line.
Points lie on the same line, if they are collinear.
Write 2 other forms
If two lines are parallel, then they
never intersect.
Lines never intersect, if they are parallel.
All parallel lines never intersect.
Converse
The converse of a conditional
statement is formed by exchanging
the hypothesis and the conclusion
in the conditional.
Not (then), if form!!!
Write the converse of the
statement
If a figure is a triangle, then it has
three angles.
As is:
H: a figure is a triangle
C: it has three angles.
Converse:
H: a figure has three angles
C: it is a triangle.
If a figure has three angles, then it is a triangle.
Write the Converse
If you are at least 16 years old, then you
can get a driver’s license.
If you can get a driver’s license, then you are
at least 16 years old.
Write the Converse
All collinear points lie on the same
line.
Need to write it in if, then form first then change
to converse.
If points are collinear, then they lie on the same line.
If points lie on the same line, then they
are collinear.
True or False?
If a figure is a square, then it has four
sides.
True
Is the converse true?
Converse: If a figure has four sides, then it is a square.
False, counterexample would be a rectangle.
Homework
Pg. 26 1 – 9 all, 10 – 36 E