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GEOMETRY CHAPTER 2
Deductive Reasoning pages 80-123
2-1 CONDITIONAL
STATEMENTS
• GOAL: Recognize conditional
statements
• GOAL: write the converse of
conditional statements
VOCABULARY
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Conditional Statement
Hypothesis
Conclusion
Converse
Truth Value
Deductive Reasoning
CONDITIONAL STATEMENT
• Contains if, then
• Has two parts
• If B is between A and C, then
AB +BC = AC.
HYPOTHESIS
• The part following “IF”
• If B is between A and C, then
AB +BC = AC.
CONCLUSION
• The part following then
• If B is between A and C, then
AB +BC = AC.
CONVERSE
• switch the hypothesis and
the conclusion
• If AB + BC = AC, then B is
between A and C.
TRUTH VALUE
• Whether a statement is true
or false
DEDUCTIVE REASONING
• Conclusion based on
statements
FOCUSING QUESTIONING
• IF A ANGLE IS A RIGHT, THEN IT’S
MEASURE IS 90 DEGREES.
– Identify the hypothesis
– Identify the conclusion
– State the converse
FOCUSING QUESTIONING
ANSWER
• IF AN ANGLE IS A RIGHT, THEN IT’S
MEASURE IS 90 DEGREES.
– Hypothesis: AN ANGLE IS RIGHT
– Conclusion: IT’S MEASURE IS 90 DEGREES
– State the converse: IF AN ANGLE’S
MEASURE IS 90 DEGREES, THEN THE
ANGLE IS RIGHT
2-2 BICONDITIONALS AND DEFINITIONS
• Standard: Write biconditionals
• Standard: Recognize good
definitions
VOCABULARY
• Biconditional
• Converse
BICONDITIONAL
• Contains “if and only if”
• A conditional and converse
combined together
FOCUSING QUESTION
• IF THREE POINTS LIE ON THE SAME
LINE, THEN THE POINTS ARE
COLLINEAR.
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Identify the hypothesis
Identify the conclusion
State the converse
State a biconditional
2-4 REASONING IN ALGEBRA
• Standard: Connect reasoning
in Algebra and Geometry
VOCABULARY
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Addition Property
Subtraction Property
Multiplication Property
Division Property
Reflexive Property
Symmetric Property
Transitive Property
Substitution Property
Distributive Property
Addition PROPERTY
• when you add the same
number to both sides
SUBTRACTION PROPERTY
• when you subtract the same
number from both sides
MULTIPLICATION PROPERTY
• When you multiply each side of
the equation by the same
number
DIVISION PROPERTY
• When you divide both sides of
the equation by the same
number
REFLEXIVE PROPERTY
• the equals sign is like a mirror
• a=a
SYMMETRIC PROPERTY
• You can change the order
• x = 5 or 5 = x
TRANSITIVE PROPERTY
• If a = b and b = c, then a = c
• You can take out what looks
alike
SUBSTITUTION PROPERTY
• When you replace
• a = b, then a + c = d or b + c = d
DISTRIBUTIVE PROPERTY
• Multiply what’s on the outside
of the parenthesis with
everything on the inside of the
parenthesis
• 5(2 + 5) = 10 + 25
FOCUSING QUESTION
• What are vertical angles?
• What are adjacent angles?
• What are complementary
angles?
• What are supplementary
angles?
2.5 PROVE ANGLES CONGRUENT
• Standard: Prove and apply
theorems about angles.
VOCABULARY
• Vertical Angles
• Supplements
• Complements
Vertical Angles
• Congruent
• Directly
across from
each other
COMPLEMENTS
• Equal 90
degrees
SUPPLEMENTS
• Equal 180
degrees