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