GEOMETRY CHAPTER 2Deductive Reasoning pages 80-123

2-1 CONDITIONAL STATEMENTS

• GOAL: Recognize conditional statements

• GOAL: write the converse of conditional statements

VOCABULARY

• 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 QUESTIONINGANSWER

• 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.

– 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

• 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