identifying whether a statement is TRUE or FALSE 5 Write the converse inverse

# Identifying whether a statement is true or false 5

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identifying whether a statement is TRUE or FALSE 5. Write the converse, inverse, contrapositive, and biconditional (if possible). Conditional: Truth Value: _______ If a polygon has three sides, then it is a triangle. Converse: Truth Value ________ _____________________________________________________________ _____________________________________________________________ Inverse: Truth Value ________ _____________________________________________________________ _____________________________________________________________ Contrapositive: Truth Value ________ _____________________________________________________________ _____________________________________________________________ Biconditional: Truth Value ________ _____________________________________________________________ U2 - 5 _____________________________________________________________ If a triangle has three ࠵?࠵?° angles, then it is an equilateral triangle. What is the truth value ? _________ Is there a counterexample ? If so, what is it? ______________________ Now write the converse of the conditional statement and determine its truth value . __________________________________________________________________ __________________________________________________________ A biconditional statement can ONLY be written if the __________________ and _______________ are TRUE. If a triangle is a right triangle, then it contains one 90° angle. True or False? ________ Converse: ____________________________________________________________ True or False? ________ Biconditional statement (if applicable) __________________________________________________________________ __________________________________________________________ *Biconditional statements are important because we will use them to discuss theorems. U2 - 6 Lesson 2.3: Deductive Reasoning and Proofs (TB 2.4-5) Deductive Reasoning : the process of reasoning that uses FACTS to form a conclusion Postulate : “rule” of geometry that is accepted as true, but has NOT been proven A theorem , unlike a postulate, is a statement that must be __________________ to be true. A proof is a ________________________________ argument that shows that a statement is __________________. Two-column proof : lists statements and reasons starting with given information and each step that leads to the conclusion in a two column format Paragraph proof : gives statements and reasons in sentence format that create a paragraph Properties of Equality Property How It Works Addition Property of Equality If ࠵? = ࠵? , then ࠵? + ࠵? = ࠵? + ࠵? . Subtraction Property of Equality If ࠵? = ࠵? , then ࠵? − ࠵? = ࠵? − ࠵? . Multiplication Property of Equality If ࠵? = ࠵? , then ࠵?࠵? = ࠵?࠵? . Division Property of Equality If ࠵? = ࠵? , then 0 1 = 2 1 where ࠵? ≠ 0 . Substitution Property If ࠵? = ࠵? , then ࠵? can be substituted for ࠵? in any equation containing ࠵? . Distributive Property ࠵?(࠵? + ࠵?) = ࠵?࠵? + ࠵?࠵? Reflexive Property of Equality ࠵? = ࠵? Symmetric Property of Equality If ࠵? = ࠵? , then ࠵? = ࠵? . Transitive Property of Equality If ࠵? = ࠵? and ࠵? = ࠵? , then ࠵? = ࠵? . ** These properties of equality will be used in both algebraic and geometric proofs. ** U2 - 7 (There are also Reflexive, Symmetric, and Transitive Properties of Congruence so be very specific when stating which one you want to use!!) Properties of Congruence Property Example: Congruence of Segments Example: Congruence of Angles Reflexive Property of Congruence ࠵?࠵? ≅ ࠵?࠵? ∠࠵? ≅ ∠࠵? Symmetric Property of Congruence If ࠵?࠵? ≅ ࠵?࠵? , then ࠵?࠵? ≅ ࠵?࠵? . If ∠࠵? ≅ ∠࠵? , then ∠࠵? ≅ ∠࠵? . Transitive Property of Congruence If ࠵?࠵? ≅ ࠵?࠵? and ࠵?࠵? ≅ ࠵?࠵? , then ࠵?࠵? ≅ ࠵?࠵? .  #### You've reached the end of your free preview.

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• Spring '14
• Logic, Transitive Property, symmetric property, Property of Equality, Reflexive Property
• • •  