Name: Period: 9/28 10/7

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Name: Period: 9/28 – 10/7

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1) I can define, identify and illustrate the following terms Transversal Corresponding angles

Alternate exterior angles

Alternate interior angles Same side interior angles

.

Dates, assignments, and quizzes subject to change without advance notice

Monday Tuesday Block Day Friday

26 27 28/29

Parallel Line Theorems 30

Angles Formed by Parallel Lines &

Transversals 3

Angles with Quadratics and Systems

Quiz

4

Parallel Line Proofs 5/6

Review

7 T

TEESSTT 44

Wednesday, 9/28/11 and Thursday, 9/29/11

Parallel Line Theorems

Can you prove the parallel line theorems without using the corresponding angles postulate? Why not? 2) I can prove the parallel line theorems.

Lines and Transversals Sketchpad Activity

ASSIGNMENT: Angles Formed by Parallel Lines and Transversals Proofs Worksheet pg. 158-161 (7-27 odd, 28, 31, 36, 45-47)

Completed:

Friday, 9/30/11

Angles Formed by Parallel Lines and Transversals (3-1 & 3-2)

What are the parallel line theorems and postulate?

3) I can apply parallel line theorems and postulates to solve problems.

ASSIGNMENT:pg. 167-169 (15, 19-21, 24-36, 46-53) Completed:

Monday, 10/3/11

Angles with Quadratics and Systems

Explain the process needed to set up a system of equations using the parallel lines and transversal.

4) I can apply parallel line theorems and postulates to solve problems with more advanced algebra.

QUIZ: Identifying Angle Pairs (Vocabulary) Grade:

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Tuesday, 10/4/11

Parallel Lines Proofs

How can using transitive property of congruence instead of the substitution property of equality save you work in a proof?

5) I can prove angle relationships using a two-column proof. 6) I can prove lines are parallel using a two-column proof.

ASSIGNMENT: Parallel Proofs Worksheet Completed:

Wednesday, 10/5/11 and Thursday 10/6/11

Review

I can assess my strengths and weaknesses of all previously learned material.

ASSIGNMENT: Design Your Own City Project (Counts as a quiz grade) Grade:

ASSIGNMENT: Review Worksheet

Friday, 10/7/11

Test 4 – Lines and Transversals

I can demonstrate knowledge skills, and reasoning ability of ALL previously learned material.

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1 2 3 4 5 6 8 7 l h t Name Period:

Angles Formed by Parallel Lines and Transversals Proofs

Definition: In the picture at right, line l is called a transversal.

Definition: For two lines intersected by a transversal, corresponding angles are a pair of angles that lie on the same side of the transversal and on the same sides of the two other lines. For example, in the picture at right, 1&5are corresponding, 2 &6are corresponding, as well as 3 &8 and 4 &7.

Corresponding Angle Postulate: If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent.

You will be using this postulate and the picture above to write the following proofs. Two of

them are completed as examples; you need to use this new postulate and the previously learned definitions, theorems, or postulates to fill in the reasons.

1. Given: t h 2. Given: t h Prove: 3≅6 _Prove:₂≅₈ Statement Reason 1. t h Given 2. 3≅8 _{Corresponding}_s_post. 3. 8≅6 4. 3≅6 3. Given: t h 4. Given: t h

Prove: 3 and 5 are supplementary Prove: 2 and 7 are supplementary

Statement Reason

1. t h

2. 3≅8 3. m3=m8

4. 8and 5are supp. 5. m8+m5=180°

6. m3+m5=180°

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Parallel Lines With Algebra

Remember – drawings are not necessarily drawn accurately!

1 – 3: Find the value of x in each question given that lines l and m are parallel. Check your answers by finding the measure of each angle.

1) 3 10; 70 m C x m F x ∠ = − ∠ = + 2) 27; 2 39 m D x m F x ∠ = + ∠ = − 3) 2( 40); 5 44 m B x m G x ∠ = + ∠ = +

4 – 6: Find the value of x in each question given that lines l and m are parallel. Check your answers by finding the measure of each angle.

4) 3 2 16; 5 7 4 m x m x ∠ = + ∠ = − 5) 4 8 80; 5 2 116 m x m x ∠ = − ∠ = − + 6) 2 3 19; 6 2( 10) m x m x ∠ = + ∠ = +

7) Given l || m || n and s || t , and m∠ =1 143°_{, find}

2 m =_{______}_m₁₁=_{______} _m₂₀=_{______} 3 m =_{______}_m₁₂=_{______} _m₂₁=_{______} 4 m =_{______}_m₁₃=_{______} _m₂₂=_{______} 5 m =_{______}_m₁₄=_{______} _m₂₃=_{______} 6 m =_{______}_m₁₅=_{______} _m₂₄=_{______} 7 m =_{______}_m₁₆=_{______} 8 m =_{______}_m₁₇=_{______} 9 m =_{______}_m₁₈=_{______} 10 m =_{______} _m₁₉=_{______} 1 2 3 4 5 6 7 8 9 10 11 12 13 14 17 18 19 20 15 16 21 22 23 24 l m n t s A B C D E F H G m l 1 2 4 3 5 6 ₇ 8

m

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8 – 10: Given l m , find the value(s) of x and each angle. Be sure to check for extraneous solutions. 8) 2 3 112; 8 16 131 m x m x ∠ = + ∠ = + 9) 2 3 2 ; 6 3 108 m x x m x ∠ = − ∠ = + 10) 2 1 7 ; 7 7 m x x m x ∠ = − ∠ = − +

11 – 13: Givenp t , find the value(s) of each variable and each angle.

11) 1 12 4 8 4 5 15 8 m x y m x y m x y ∠ = − ∠ = − ∠ = + 12) 2 8 5 7 25 4 3 5 m b a m a b m a b ∠ = + ∠ = + ∠ = + 13) 3 14 3 7 9 12 4 5 6 m s t m s t m s t ∠ = − ∠ = + ∠ = +

14) Given that m∠4=3x+10_and_m∠₁₂=₂_x+₃₀_{, find the value of}_x_,_m∠_4,_m∠_10.

Write a two-column proof.

15) Given:l m

Prove: 1and 2 are supplementary 16) Given:l m anda b Prove: 1≅12 1 2 4 3 5 6 8 7

l

m

l m 1 2 3 1 2 3 4 5 ₆ 7 8 12 11 9 10 15 16 ₁₃14 a b m l 1 2 4 3 5 6 8 7 p t 1 2 3 4 5 ₆ 7 8 12 11 9 10 15 16 ₁₃14

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Name: Per:

Parallel Proofs Worksheet

Instructions: On a separate piece of paper, write a two-column proof for each problem.

1. Given: 2. Given: ∠1_and∠₅_{are supplementary}

Prove: l m

Prove: p q

3. Given:

Prove: 15and 6are supplementary

4. Given: 1 3 1 2 m m m m ∠ = ∠ ∠ = ∠ Prove: m∠ =3 m∠4

5.Given: ∠1&∠4_{are supplementary} q r Prove: p q 6. Given: HJ LM HG LK Prove: m∠5=m∠8 1 2 3 4 5 l m 7 8 p q t

7

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8

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12

m

x

m

x

∠

=

−

∠ =

+

=

1 2 3 4 5 6 7 8 12 11 9 10 15 16 ₁₃14 a b m l

,

a b l m

B A C D 1 2 E 3 4 G H J M L Q K 5 6 7 8 1 2 3 4 t p q r s

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Name:_______________________________ Period:______

Review: Parallel Lines and Transversals

Each learning target has one example problem listed in part (a). Solve it, then go back to your assignments, find a similar problem (or make up your own), write it down and solve it in part (b).

I can define, identify and illustrate the vocabulary words from my unit plan. See Tuesday’s quiz for examples of vocabulary questions.

For questions 1–8, solve for the variable(s) and find all angle measures. Use them to check your work!

I can apply parallel line theorems and postulates to solve problems. 1. a. 1 (30 33) 2 (20 58) m x m x = + ° = + ° 2. a. 3. a. 4. a.

I can apply parallel line theorems and postulates to solve problems with advanced algebra.

5. a. 2 1 ( 94) 2 (5 62) m x m x = + ° = + ° 6. a. b. b. b. b. b. b.

>

1 2

>

> > (7x−20)° (5x+6)° (4x+53)° (6x−28)°

>

2 (3x +11 )x° 2 (2x −18)° (2x+29)° (10x+45)° a b _{a b} k l 1 2 k l

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7. 8. a. 9. a. 1 (14 8 ) 2 (7 7 ) 3 (12 2 ) m x y m x y m x y

p q

= + ° = + ° = − °

I can prove angle relationships using a two-column proof.

10. a. Given: a b l m ;

Prove: 6≅16

I can prove lines parallel using a two-column proof. 11. a. Given: 2 and 8 are supplementary.

Prove: m n b. b. b. b. (2x+5 )y° > > (22x+4 )y ° (18x+3 )y° 1 2 3 p q 1 2 3 4 5 6 7 8 12 11 9 10 15 16 ₁₃14 a b m l 1 2 5 6 7 8 3 4 m n