WELCOME BACK! AGENDA FOR TODAY: ACT WARM UP RETURN TESTS START SECTION 3.1

LESSON 3-1 LEARNING TARGETS I can identify the relationships between lines and planes I can name angles formed by parallel lines and transversals

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

AEADBFBC EFDC HG EHDHFGCG

a line that intersects two or more lines in a plane transversal

∠3, ∠4, ∠5, ∠6 ∠1, ∠2, ∠7, ∠8

∠4 and ∠5 ∠3 and ∠6 ∠1 and ∠8 ∠2 and ∠7

∠4 and ∠6 ∠3 and ∠5 ∠1 and ∠7 ∠2 and ∠8 ∠1 and ∠5 ∠2 and ∠6 ∠3 and ∠7 ∠4 and ∠8

WARM UP 1.NAME ALL THE LINES PARALLEL TO AD. (2) 2.NAME THE PLANE PARALLEL TO ADC. (1) 3.NAME THE LINES THAT INTERSECTS WITH AD. (4) 4.NAME THE PLANES THAT INTERSECTS WITH ADC. (4) 5.NAME A LINE SKEW TO AD. 6.NAME A LINE SKEW TO AB

AIA AEA CA CIA AEA AIA CIACA AEA CA AIA

AEA AIA CIA CA AEA AIA CA

FG CDCBGHGF DHBF AE ABEF ADEH

ASSIGNMENT: 3.1 WORKSHEET

LESSON 3-2 LEARNING TARGETS I can use properties of parallel lines to find angle measures. I can use properties of parallel lines to determine congruent angles

l ∥ m m l

congruent ∠1 ≅ ∠5 ∠2 ≅ ∠6 ∠3 ≅ ∠7 ∠4 ≅ ∠8

congruent ∠3 ≅ ∠6 ∠4 ≅ ∠5

congruent ∠1 ≅ ∠8 ∠2 ≅ ∠7

supplementary m∠3 + m∠5 = 180 m∠4 + m∠6 = 180

125° 55°

92° 74° 92° 88° 106° 74°

78° 102° 78° 102°

2x – 10= x + 15 x – 10 = 15 x = 25 m∠5 = 2(25) – 10 m∠6 = = 40°

9x + 12= 42 9x = 30 x = 3 1/3 m∠1 = 9(3 1/3 ) + 12 = 42°

8x – 6+ 6x x + 40 = x = 140 = 180 x = m∠4 = 6(10) +46 = 106° 106°

9y – y = 180 9y = 79 = 180 y = ° x = 10, y = 8.78

9a + 6= 10a – 6 6 = a – 6 12 = a m∠2 = 10(12) – 6 = 114° 114°

5b + 14= 114 5b = 100 b = ° a = 12, b = 20

80° 68°80° 100° 68° 112°

8x – 10= 7x x = 10 70° 6y = 180 6y + 90 = 180 6y = 90 y = 15

WARM UP

Learning Target Check! Section 3.1 I can identify the relationships between lines and planes I can name angles formed by parallel lines and transversals Section 3.2 I can use properties of parallel lines to find angle measures. I can use properties of parallel lines to determine congruent angles

LESSON 3-3 LEARNING TARGETS I can find slopes of lines I can use slope to determine if lines are parallel or perpendicular

rise run m = y 2 – y 1 x 2 – x 1 rise run

m = m = 2 – – -3 m = 4 2 = 2 m = y 2 – y 1 x 2 – x 1

m = y 2 – y 1 x 2 – x 1 m = – 0 m = 0 – – 0 m = 1 -4 = – 1 4

m = 5 – 5 -3 – 1 m = 0 -4 = 0 Horizontal lines always have slope = 0! m = y 2 – y 1 x 2 – x 1

m = -4 – 3 6 – 6 m = -7 0 = undefined Vertical lines always have undefined slope! m = y 2 – y 1 x 2 – x 1

Have equal slopes m = 3/4

Have opposite, reciprocal slopes m = 3/4 m = -4/3

m = 7 – -5 4 – -2 Slope of AB: m = 12 6 = 2 m = -2 – 2 8 – 0 Slope of CD: m = -4 8 = – 1 2 perpendicular

neither parallel neither perpendicular

WARM UP

LESSON 3-4 LEARNING TARGETS I can construct perpendicular lines through a point. I can construct parallel lines through a point.

REVIEW!

CONSTRUCTIONS Complete the remaining constructions using the directions on your table. Follow the steps carefully!

ASSIGNMENT: WORKSHEET!

Learning Target Check! Section 3.3 I can find slopes of lines. I can use slope to identify parallel lines. I can use slope to identify perpendicular lines. Section 3.4 I can construct parallel and perpendicular lines.

LESSON 3-5 LEARNING TARGETS I can prove that lines are parallel based on given angle relationships I can prove that angles are congruent or supplementary based on parallel lines.

congruent parallel CA ≅ → || lines

congruent parallel AIA ≅ → || lines

congruent parallel AEA ≅ → || lines

supplementary parallel CIA supplementary → || lines

AIA ≅ → || lines

CA ≅ → || lines

CIA supplementary → || lines

AEA ≅ → || lines

AIA ≅ → || lines

Given Transitive AIA ≅ → || lines

ASSIGNMENT: 3.5 Worksheet

WARM UP ACTIVITY… HAVE OUT… 1)YOUR GOLDEN FOLDABLE FROM YESTERDAY 2)THE STACK OF ANGLE PAIR CARDS ON YOUR TABLES. DIRECTIONS: WHEN I SHOW A DIAGRAM, HOLD UP THE CARD WITH THE CORRECT ANGLE PAIRING. USE YOUR FOLDABLE IF YOU ARE UNSURE!

2 10

16 6

10 4

16 7

10 8 BONUS… A LITTLE TRICKY…

0. l ∥ m 0. Given 1. ∠10 ≅ ∠16 1. || lines → AEA ≅

1. r ∥ s 0. Given 0. ∠2 ≅ ∠12 1. AIA ≅ → || lines

0. l ∥ m 0. Given 1. m∠3 + m∠6 = || lines → CIA supp

1. r ∥ s 0. Given 0. ∠7 ≅ ∠15 1. CA ≅ → || lines

0. p ∥ q 1. m ∥ n 0. Given 1. Given 2. ∠4 ≅ ∠6 3. ∠6 ≅ ∠5 4. ∠4 ≅ ∠5 2. || lines → CA ≅ 3. || lines → CA ≅ 4. Transitive

1. Name a pair of Alternate Interior Angles (AIA). 2. Name a pair of Corresponding Angles (CA) A. ∠5, ∠13B. ∠8, ∠14C. ∠6, ∠16D. ∠7, ∠14 F. ∠3, ∠4G. ∠3, ∠9H. ∠3, ∠13J. ∠3, ∠7 3. Name a pair of Consecutive Interior Angles (CIA). A. ∠7, ∠14B. ∠3, ∠11C. ∠2, ∠12D. ∠7, ∠8

Explain how you would find the measures of the numbered angles in this figure. Use complete sentences. 115° 65° 2 3 4