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Unit 2 – Intro to Geometry Pre-AP Geometry – Schwarz Before Learning ______ ______ ______ ______ ______ ______ ______ ______ Date Wed 9/9 Thursday 9/10 Friday 9/11 Monday 9/14 Tuesday 9/15 Wed. 9/16 Thursday 9/17 Friday 9/18 Monday 9/21 Objective After Learning Use logical arguments. Conditional and Converses Statements. (book 2.2) Determine the truth values of inverses and contrapositives. (book 2.2) LTF LR Use logical reasoning skills (inductive and deductive) to make and test conjectures. Formulate Counterexamples. (book 2.1 and 2.3) Use postulates involving points, lines and planes. (book 2.4) Use algebraic properties in logical arguments. (+. -. *, /, substitution, distributive, reflexive, symmetric, and transitive) (book 2.5) Prove geometric theorems. (book 2.6) Learn and apply properties of special angle pairs. (book 2.7) Topics Covered Present IF/THEN posters Converse, Inverse, Contrapositive, Bi-conditional Grade Picasso Polygons Truth Tables Use deductive reasoning to form a logical argument. Law of Syllogism and Law of Det. The 7 important postulates Properties from Algebra: +, -, *, /, substitution, distributive, Reflexive, Symmetric, Transitive Proofs and Angle Pair Relationships Proofs and Angle Pair Relationships Review UNIT 2 TEST Assignment Bi-conditional Negation Counter-example Perpendicular Lines ______ ______ Grade Homework – from notes HW 2.1 pg 82 8-24 all Please write neatly ____/____ HW 2.2 pg 90 4-13, 16-19, 30-35 ____/____ HW 2.3 pg 99 4-24 Even, 46, 48, 50, 56 ____/____ Class activity HW 2.4 pg 108 1-5 all, 6-20 even, 21-30 ____/____ HW 2.5 pg 116 3-12, 16, 21-24, 32-34 HW 2.6 pg 128-129 834 even, 37, 38, 49-53 TBD Notebooks Due Unit 2 Vocabulary Conditional Converse Inverse Contrapositive _______ _______ _______ _______ _______ _______ Law of Syllogism Law of Detachment Postulate ____/____ ____/____ ____/____ Unit 2 – Intro to Geometry Pre-AP Geometry – Schwarz Before Learning ______ ______ ______ ______ ______ ______ ______ ______ Date Wed 9/9 Thursday 9/10 Friday 9/11 Monday 9/14 Tuesday 9/15 Wed. 9/16 Thursday 9/17 Friday 9/18 Monday 9/21 Objective After Learning _______ _______ _______ _______ _______ _______ Use logical arguments. Conditional and Converses Statements. (book 2.2) Determine the truth values of inverses and contrapositives. (book 2.2) LTF LR Use logical reasoning skills (inductive and deductive) to make and test conjectures. Formulate Counterexamples. (book 2.1 and 2.3) Use postulates involving points, lines and planes. (book 2.4) Use algebraic properties in logical arguments. (+. -. *, /, substitution, distributive, reflexive, symmetric, and transitive) (book 2.5) Prove geometric theorems. (book 2.6) ______ ______ Learn and apply properties of special angle pairs. (book 2.7) Topics Covered Present IF/THEN posters Converse, Inverse, Contrapositive, Bi-conditional Grade Picasso Polygons Truth Tables Use deductive reasoning to form a logical argument. Law of Syllogism and Law of Det. The 7 important postulates Properties from Algebra: +, -, *, /, substitution, distributive, Reflexive, Symmetric, Transitive Proofs and Angle Pair Relationships Proofs and Angle Pair Relationships Review UNIT 2 TEST Assignment Grade Homework – from notes HW 2.1 pg 82 8-24 all Please write neatly ____/____ HW 2.2 pg 90 4-13, 16-19, 30-35 ____/____ HW 2.3 pg 99 4-24 Even, 46, 48, 50, 56 ____/____ Class activity HW 2.4 pg 108 1-5 all, 6-20 even, 21-30 ____/____ HW 2.5 pg 116 3-12, 16, 21-24, 32-34 HW 2.6 pg 128-129 834 even, 37, 38, 49-53 TBD ____/____ ____/____ ____/____ Notebooks Due Unit 2 Vocabulary Conditional Converse Inverse Contrapositive Bi-conditional Negation Counter-example Perpendicular Lines Law of Syllogism Revised 6/29/2016 Law of Detachment Postulate Postulates Postulate 5 Postulate 6 Postulate 7 Postulate 8 Postulate 9 Postulate 10 Postulate 11 Through any two points there exists exactly one line. A line contains at least two points. If two lines intersect, then their intersection is exactly one point Through any three non-collinear points there exists exactly one plane. A plane contains at least three non-collinear points. If two points lie in a plane, there the line containing them lies in the plane. If two planes intersect, then their intersection is a line. Properties from Algebra Addition Property If a = Subtraction Property If a = Multiplication Property If a = Division Property If a = Substitution Property Distributive Property b, then a + c = b + c b, then a – c = b – c b, then ac = bc a b . c c If a = b, then a can be substituted for b in any equation or expression. a(b + c) = ab + ac, where a, b, and c are real numbers. b and c ≠ 0, then Properties of Equalities Reflexive Property Real Numbers Segment Length Angle Measures Symmetric Property For any real number a, a = a. For any real numbers a and b, if a = b, then b = a. For any segment AB, AB = AB. For any segments AB and CD, if AB = CD, then CD = AB. For any angle A, mA = mA. For any angles A and B, if mA = mB, then mB = mA. Transitive Property For any real numbers a, b, and c, if a = b and b = c, then a = c. For any segments AB, CD,and EF, if AB = CD, and CD = EF, then AB = EF. For any angles A, B, & C if mA = mB and mB = mC, then mA = mC. Revised 6/29/2016