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Published byIwan Atmadjaja Modified over 6 years ago
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Lesson 3-1 I can identify relationships between two lines or planes
I can name angles formed by a pair of lines and a transversal Lesson 3-1
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lines that are coplanar and don’t intersect
lines that are not coplanar and don’t intersect planes that don’t intersect
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6 plane DCG plane DAE
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BC AD CG
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AE AD BF BC EF DC HG EH DH FG CG
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a line that intersects two or more lines in a plane
transversal
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∠3, ∠4, ∠5, ∠6 ∠1, ∠2, ∠7, ∠8
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∠4 and ∠5 CIA ∠3 and ∠6 ∠1 and ∠8 CEA ∠2 and ∠7
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∠4 and ∠6 ∠3 and ∠5 ∠1 and ∠7 ∠2 and ∠8 ∠1 and ∠5 ∠2 and ∠6 ∠3 and ∠7
AIA ∠1 and ∠7 AEA ∠2 and ∠8 ∠1 and ∠5 ∠2 and ∠6 CA ∠3 and ∠7 ∠4 and ∠8
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AIA CIA AEA CIA AIA AEA CIA CA CA CIA AEA AIA
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AIA CA AEA CIA AEA AIA CA
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FG CD CB GH GF DH BF AE AB EF AD EH
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ASSIGNMENT: 3-1 worksheet
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I can use properties of parallel lines to determine if angles are congruent
Lesson 3-2
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l l ∥ m m
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congruent
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congruent
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congruent
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supplementary m∠3 + m∠5 = 180 m∠4 + m∠6 = 180
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125° 55° 55° 125° 55° 55° 125° 125° 125° 55° 55° 55° 125°
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92° 106° 92° 74° 92° 106° 88° 74° 106°
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80° 100° 80° 68° 80° 68° 100° 112°
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2x – 10 = x + 15 x – 10 = 15 x = 25 m∠5 = 40 m∠6 = 40
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9x + 12 + 42 = 180 9x + 54 = 180 9x = 126 x = 14 m∠1 = 138
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74° 106° 8x – 6 + 6x + 46 = 180 + 6x + 46 14x = 140 9y – 7 = 74 9y = 81 x = 10 y = 9
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80° 100° 80° 68° 112° 100°
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8x – 10 = 7x 70° x = 10 6y + 20 + 70 = 180 6y + 90 = 180 6y = 90 y = 15
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ASSIGNMENT: 3-2 worksheet
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Lesson 3-3 I can find the slopes of lines
I can use slopes to determine if lines are parallel or perpendicular Lesson 3-3
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rise run run rise m = y2 – y1 x2 – x1
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m = y2 – y1 x2 – x1 m = 2 – -2 -1 – -3 m = 2 + 2 -1 + 3 m = 4 2 = 2
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rise m = run m = -1 4 m = 1 -4 = – 1 4
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y2 – y1 m = x2 – x1 m = 5 – 5 -3 – 1 m = -4 = 0
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rise m = run m = 7 = undefined
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m = -3/5 Have equal slopes m = -3/5
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m = -3/5 Have opposite, reciprocal slopes m = 5/3
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perpendicular Slope of AB: Slope of CD: m = 7 – -5 4 – -2 m = -2 – 2 8 – 0 m = 12 6 m = -4 8 = – 1 2 = 2
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neither parallel neither perpendicular
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ASSIGNMENT: 3-3 worksheet
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I can prove that two lines are parallel based on given angle relationships
Lesson 3-4
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congruent parallel
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congruent parallel
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congruent parallel
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supplementary parallel
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AIA ≅ ↔ || lines
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CIA supplementary ≅ ↔ || lines
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Not a common transversal
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∠3 ≅ ∠1 Given a || b Given CA ≅ → || lines ∠1 ≅ ∠2 ∠3 ≅ ∠2 Transitive c || d AEA ≅ → || lines
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Given Given Transitive AIA ≅ → || lines
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ASSIGNMENT: 3-5 worksheet
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