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Unit 2: Congruence, Similarity, & Proofs
Vocabulary Builder
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Vocabulary Builder Plane Parallel Lines Alternate Exterior Angles
Same-Side Interior Angles Skew Lines Corresponding Angles Transversal Parallel Lines Alternate Interior Angles
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Vocabulary Builder Congruent Statement Angle Measure
Congruent Polygons Congruent Segments Congruent Triangles Proof Algebraic Equation Segment Measure Congruent Angles
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Vocabulary Builder Addition Property Reflexive Property
Division Property Transitive Property Symmetric Property Multiplication Property Distributive Property Subtraction Property Substitution Property
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Vocabulary Builder Congruent Complements Theorem
Vertical Angles Theorem Congruent Supplements Theorem All right angles are congruent If two angles are congruent and supplementary, then each is a right angle
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Unit 2: Congruence, Similarity, & Proofs
2.8 Parallel Lines and Transversals
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2.8 Parallel Lines and Transversals
Daily Agenda Transversal Lie between the two lines 3, 4, 5, 6 On opposite sides of the transversal 3 and 6, 4and 5 On same side of the transversal 3 and 5, 4 and 6 Lie outside the two lines 1, 2, 7, 8 On opposite sides of the transversal 1 and 8, 2 and 7
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2.8 Parallel Lines and Transversals
Daily Agenda
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Daily Agenda Consecutive Interior Vertical Alternate Interior
Alternate Exterior Consecutive Interior Vertical Alternate Exterior Alternate Exterior Vertical Consecutive Interior Vertical Alternate Interior
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45 45 135 135 Daily Agenda Alternate Interior angles are congruent
Vertical angles are congruent 135 135 Consecutive interior angles are supplementary Linear pairs are supplementary
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2.8 Parallel Lines and Transversals
Daily Agenda Corresponding Angles Alternate Interior Angles Alternate Exterior Angles Consecutive Supplementary
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𝑚∠1= ______ 𝑚∠2=________ 𝑚∠3=_______ 𝑚∠4=________ 𝑚∠5=________
𝑚∠6=________ 𝑚∠7=________ 102 𝑚∠8= ______ 𝑚∠9=________ 𝑚∠10=_______ 𝑚∠11=________ 𝑚∠12=________ 𝑚∠13=________ 𝑚∠14=________ 102 𝑚∠1= ______ 𝑚∠2=________ 𝑚∠3=_______ 𝑚∠4=________ 𝑚∠5=________ 𝑚∠6=________ 𝑚∠7=________ 40 𝑚∠1= ______ 𝑚∠2=________ 𝑚∠3=_______ 𝑚∠4=________ 𝑚∠5=________ 𝑚∠6=________ 35 𝑚∠7= ______ 𝑚∠8=________ 𝑚∠9=_______ 𝑚∠10=________ 𝑚∠11=________ 𝑚∠12=________ 65 78 78 140 80 115 102 102 140 80 65 78 78 40 100 115 102 102 140 65 100 78 102 140 65 80 102 78 40
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Daily Agenda
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2.8 Parallel Lines and Transversals
Daily Agenda
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2.8 Parallel Lines and Transversals
Daily Agenda
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Daily Agenda Direct Explanation Worktime Closing
Unit 2: Similarity, Congruence, and Proofs Warm-up Parallel Lines and Transversals Notes with Guided Practice Checking for Understanding Direct Explanation Parallel Lines and Transversals Independent Practice Students will complete questions #1 – 10 Worktime How can I apply all that I have learned about Parallel Lines and Transversals to demonstrate mastery of the standards? Closing
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Unit 2: Congruence, Similarity, & Proofs
2.9 Introduction to Proofs
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2.9 Introduction to Proofs
Daily Agenda proof theorem given definition theorem Mathematical property statements reasons given prove postulate Undefined terms
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2.9 Introduction to Proofs Daily Agenda
If a = b, then a + c = b + c If a = b, then a – c = b – c If a = b, then a · c = b · c If a = b, and c ≠ 0, then 𝒂 𝒄 = 𝒃 𝒄 a (b + c) = ab + ac a = a If a = b and b = c, then a = c If a = b, then b = a If a = b, the b can replace a in any expression If a + (b + c) = (a + b) + c If a + b = b + a
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2.9 Introduction to Proofs
Daily Agenda Transitive Property Subtraction Property Reflexive Property Multiplication Property TRS 2 + BC
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2.9 Introduction to Proofs
Daily Agenda Symmetric Property Substitution Property Subtraction Property Transitive Property BKC TES 30˚
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2.9 Introduction to Proofs
Daily Agenda Addition Property Division Property Distributive Property Addition Property Division Property Symmetric Property
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2.9 Introduction to Proofs
Daily Agenda 4 = x Addition Property -12 = 4x Subtraction Property -3 = x Division Property
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2.9 Introduction to Proofs
Daily Agenda
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2.9 Introduction to Proofs
Daily Agenda
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Unit 2: Congruence, Similarity, & Proofs
2.10 Prove Theorems about Lines and Angles
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2.10 Prove Theorems about Lines and Angles
Daily Agenda 𝑨𝑩 ≅ 𝑨𝑪
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2.10 Prove Theorems about Lines and Angles
Daily Agenda Given Definition of congruent segments Reflexive Property Segment Addition Postulate Segment Addition Postulate Substitution Property Definition of congruent segments
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2.10 Prove Theorems about Lines and Angles
Daily Agenda Given Definition of Linear Pair Linear Pair Theorem Definition of supplementary angles Substitution Property Subtraction Property
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2.10 Prove Theorems about Lines and Angles
Daily Agenda Given Definition of Linear Pair Definition of opposite rays Angle Addition Postulate Definition of Supplementary Given Alternate Interior Vertical Angles Theorem Substitution Property
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2.10 Prove Theorems about Lines and Angles
Daily Agenda
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Unit 2: Congruence, Similarity, & Proofs
2.11 Prove Theorems about Triangles
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2.11 Prove Theorems about Triangles
Daily Agenda CPCTC Reflexive Property SSS Congruence Vertical Angles Theorem SAS Congruence
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2.11 Prove Theorems about Triangles
Daily Agenda Given Given Alternate Interior Angles Reflexive Property SAS Congruence
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2.11 Prove Theorems about Triangles
Daily Agenda 𝑻𝑸 ≅ 𝑹𝑸 Vertical Angles Theorem SAS Congruence 𝑼𝑾 ≅ 𝑼𝑾 Isosceles Triangle Theorem AAS Congruence
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2.11 Prove Theorems about Triangles
Daily Agenda Given 𝑿𝑰 ≅ 𝑴𝑰 Given ∠𝑿𝑰𝑨 ≅∠𝑴𝑰𝑶 Vertical Angles Theorem SAS Congruence Given Alternate Interior Angles Given Vertical Angles Theorem ASA Congruence
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2.11 Prove Theorems about Triangles
Daily Agenda
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Unit 2: Congruence, Similarity, & Proofs
2.12 Prove Theorems about Parallelograms
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2.12 Prove Theorems about Parallelograms
Daily Agenda Alternate Interior Angles Reflexive Property AAS Congruence Given Def. of parallelogram Alternate Interior Reflexive Property ∆𝑨𝑩𝑫 ≅∆𝑪𝑫𝑩 CPCTC
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2.12 Prove Theorems about Parallelograms
Daily Agenda Alternate Interior Angles Reflexive Property ASA Congruence
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2.12 Prove Theorems about Parallelograms
Daily Agenda
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