GEOMETRY CHAPTER 2 Deductive Reasoning pages

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 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. –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) =

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