Download Geometry Section 2-2: Conditional Statements A conditional

Geometry
Section 2-2: Conditional Statements
A conditional statement is a statement that can be written in “if-then” form.
For example, “If it is raining outside, then I will carry an umbrella.” is a conditional statement.
The hypothesis is the “if” part of the statement. (It is raining outside…)
The conclusion is the “then” part of the statement. (…I will carry an umbrella)
Ex. 1: Identify the hypothesis and conclusion of each.
a) If today is Halloween, then it is October.
Hypothesis: Today is Halloween.
Conclusion: It is October.
b) A number is a rational number if it is an integer.
Hypothesis: A number is an integer.
Conclusion: It’s a rational number.
Ex. 2: Write as a true conditional statement.
a) An obtuse triangle has exactly one obtuse angle.
If a triangle is obtuse, then it has exactly one obtuse angle.
b) Congruent angles have equal measures.
If angles are congruent, then they have equal measures.
c)
d)
birds
blue
jays
If an animal is a blue jay, then it is a bird.
quadrilaterals
rectangles
If a figure is a rectangle, then it is a quadrilateral.
Remember our original conditional statement: “If it is raining outside, then I will carry an
umbrella.”
Hypothesis: It is raining outside.
Conclusion: I will carry an umbrella.
The converse is formed by switching the hypothesis and conclusion.
“If I am carrying an umbrella, then it is raining outside.”
The inverse is formed by negating (making opposite) the hypothesis and conclusion.
“If it is not raining outside, then I will not carry an umbrella.”
The contrapositive is formed by switching the hypothesis and conclusion and negating both.
“If I am not carrying umbrella, then it is not raining outside.”
Ex. 3: Write the converse, inverse, and contrapositive of each statement, and determine whether
each is true or false.
a) If an angle measures 90°, then it is a right angle. (True)
Converse: If an angle is a right angle, then it measures 90°. (True)
Inverse: If an angle does not measure 90°, then it is not a right angle. (True)
Contrapositive: If an angle is not a right angle, then it doesn’t measure 90°. (True)
b) If A is between B and C, then A is on BC . (True)
Converse: If A is on BC , then A is between B and C. (False)
Inverse: If A is not between B and C, then A is not on BC . (False)
Contrapositive: If A is not on BC , then A is not between B and C. (True)
c) If two angles are adjacent, then they form a linear pair. (False)
Converse: If two angles form a linear pair, then they are adjacent. (True)
Inverse: If two angles are not adjacent, then they don’t form a linear pair. (True)
Contrapositive: If two angles are not a linear pair, then they aren’t adjacent. (False)