PROVING PARALLELISM

GIVEN: P║Q TRANSVERSAL ℓ CUTS P AND Q Prove: <1 ≡ <2

Write the corresponding postulates as reasons:

Statements Reasons1. p║q

2. <3 ≡ <2

3. <1 ≡ <3

4. <1 ≡ <2

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GIVEN: P║Q TRANSVERSAL ℓ CUTS P AND Q Prove: <1 ≡ <2

Write the corresponding postulates as reasons:

Statements Reasons1. p║q Given2. <3 ≡ <2

3. <1 ≡ <3

4. <1 ≡ <2

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GIVEN: P║Q TRANSVERSAL ℓ CUTS P AND Q Prove: <1 ≡ <2

Write the corresponding postulates as reasons:

Statements Reasons1. p║q Given2. <3 ≡ <2 Corresponding Angle Postulate3. <1 ≡ <3

4. <1 ≡ <2

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GIVEN: P║Q TRANSVERSAL ℓ CUTS P AND Q Prove: <1 ≡ <2

Write the corresponding postulates as reasons:

Statements Reasons1. p║q Given2. <3 ≡ <2 Corresponding Angle Postulate3. <1 ≡ <3 Vertical Angles Postulate4. <1 ≡ <2

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GIVEN: P║Q TRANSVERSAL ℓ CUTS P AND Q Prove: <1 ≡ <2

Write the corresponding postulates as reasons:

Statements Reasons1. p║q Given2. <3 ≡ <2 Corresponding Angle Postulate3. <1 ≡ <3 Vertical Angles Postulate4. <1 ≡ <2 Transitive Property

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GIVEN: P║Q TRANSVERSAL ℓ CUTS P AND Q Prove: <1 and <2 are supplementary

Write the corresponding postulates as reasons:

Statements Reasons1. p║q Given2. <2 and <3 are supplementary Linear Pair3. <1 ≡ <3 Alternate Interior Angle4. <1 and <2 are supplementary Linear Pair

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LET’S TRY Letter A, page 307. In the given figure, name the postulate or theorem that justifies each statement, given m ║ n.

Statements Reasons1. <2 ≡ <8

2. <3 ≡ <7

3. <1 ≡ <3

4. <3 and <8 are supplementary5. <1 ≡ <7

6. <4 and <7 are supplementary7. There exists a line through P parallel to line n 8. a ┴b

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Statements Reasons1. <2 ≡ <8 Alternate interior angles2. <3 ≡ <7

3. <1 ≡ <3

4. <3 and <8 are supplementary5. <1 ≡ <7

6. <4 and <7 are supplementary7. There exists a line through P parallel to line n 8. a ┴b

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Statements Reasons1. <2 ≡ <8 Alternate interior angles2. <3 ≡ <7 Corresponding angle postulate3. <1 ≡ <3

4. <3 and <8 are supplementary5. <1 ≡ <7

6. <4 and <7 are supplementary7. There exists a line through P parallel to line n 8. a ┴b

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Statements Reasons1. <2 ≡ <8 Alternate interior angles2. <3 ≡ <7 Corresponding angle postulate3. <1 ≡ <3 Vertical Angles Postulate4. <3 and <8 are supplementary5. <1 ≡ <7

6. <4 and <7 are supplementary7. There exists a line through P parallel to line n 8. a ┴b

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Statements Reasons1. <2 ≡ <8 Alternate interior angles2. <3 ≡ <7 Corresponding angle postulate3. <1 ≡ <3 Vertical Angles Postulate4. <3 and <8 are supplementary Same Side of the transversal are

supplementary5. <1 ≡ <7

6. <4 and <7 are supplementary7. There exists a line through P parallel to line n 8. a ┴b

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Statements Reasons1. <2 ≡ <8 Alternate interior angles2. <3 ≡ <7 Corresponding angle postulate3. <1 ≡ <3 Vertical Angles Postulate4. <3 and <8 are supplementary Same Side of the transversal are

supplementary5. <1 ≡ <7 Alternate Exterior Angles6. <4 and <7 are supplementary7. There exists a line through P parallel to line n 8. a ┴b

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Statements Reasons1. <2 ≡ <8 Alternate interior angles2. <3 ≡ <7 Corresponding angle postulate3. <1 ≡ <3 Vertical Angles Postulate4. <3 and <8 are supplementary Same Side of the transversal are

supplementary5. <1 ≡ <7 Alternate Exterior Angles6. <4 and <7 are supplementary Same Side of the transversal are

supplementary7. There exists a line through P parallel to line n 8. a ┴b

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Statements Reasons1. <2 ≡ <8 Alternate interior angles2. <3 ≡ <7 Corresponding angle postulate3. <1 ≡ <3 Vertical Angles Postulate4. <3 and <8 are supplementary Same Side of the transversal are

supplementary5. <1 ≡ <7 Alternate Exterior Angles6. <4 and <7 are supplementary Same Side of the transversal are

supplementary7. There exists a line through P parallel to line n

Parallel Postulate

8. a ┴b

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Statements Reasons1. <2 ≡ <8 Alternate interior angles2. <3 ≡ <7 Corresponding angle postulate3. <1 ≡ <3 Vertical Angles Postulate4. <3 and <8 are supplementary Same Side of the transversal are

supplementary5. <1 ≡ <7 Alternate Exterior Angles6. <4 and <7 are supplementary Same Side of the transversal are

supplementary7. There exists a line through P parallel to line n

Parallel Postulate

8. a ┴b Perpendicular Transversal Theorem

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QUIZ Page 296-312

QUIZ: 1. Given: r║p prove <2 ≡ <3

Statements Reasons1. r ║ s2. <2 ≡ <1

3. <1 ≡ <3

4. <2 ≡ <3

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QUIZ: 2. Refer to the figure. Name the postulate or theorem used in the following statementStatements Reasons

1. <1 ≡ <2

2. <3 ≡ <4

3. <1 and <5 are supplementary4. <8 ≡ <9

5. <9 and <10 are supplementary6. <2 ≡ <3

7. <5 and <7 are supplementary 8. m<3 + m<9 = 180º9. <6 ≡ <9

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ANSWERS TO QUIZ Page 296-312

QUIZ: 1. Given: r║p prove <2 ≡ <3

Statements Reasons1. r ║ s2. <2 ≡ <1

3. <1 ≡ <3

4. <2 ≡ <3

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QUIZ: 1. Given: r║p prove <2 ≡ <3

Statements Reasons1. r ║ s Given2. <2 ≡ <1

3. <1 ≡ <3

4. <2 ≡ <3

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QUIZ: 1. Given: r║p prove <2 ≡ <3

Statements Reasons1. r ║ s Given2. <2 ≡ <1 Vertical Angles3. <1 ≡ <3

4. <2 ≡ <3

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QUIZ: 1. Given: r║p prove <2 ≡ <3

Statements Reasons1. r ║ s Given2. <2 ≡ <1 Vertical Angles3. <1 ≡ <3 Same Side of the Transversal4. <2 ≡ <3

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QUIZ: 1. Given: r║p prove <2 ≡ <3

Statements Reasons1. r ║ s Given2. <2 ≡ <1 Vertical Angles3. <1 ≡ <3 Same Side of the Transversal4. <2 ≡ <3 Transitive Property

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QUIZ: 2. Refer to the figure. Name the postulate or theorem used in the following statementStatements Reasons

1. <1 ≡ <2

2. <3 ≡ <4

3. <1 and <5 are supplementary4. <8 ≡ <9

5. <9 and <10 are supplementary6. <2 ≡ <3

7. <5 and <7 are supplementary 8. m<3 + m<9 = 180º9. <6 ≡ <9

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QUIZ: 2. Refer to the figure. Name the postulate or theorem used in the following statementStatements Reasons

1. <1 ≡ <2 Alternate interior Angles2. <3 ≡ <4

3. <1 and <5 are supplementary4. <8 ≡ <9

5. <9 and <10 are supplementary6. <2 ≡ <3

7. <5 and <7 are supplementary 8. m<3 + m<9 = 180º9. <6 ≡ <9

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QUIZ: 2. Refer to the figure. Name the postulate or theorem used in the following statementStatements Reasons

1. <1 ≡ <2 Alternate interior Angles2. <3 ≡ <4 Corresponding Angle3. <1 and <5 are supplementary4. <8 ≡ <9

5. <9 and <10 are supplementary6. <2 ≡ <3

7. <5 and <7 are supplementary 8. m<3 + m<9 = 180º9. <6 ≡ <9

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QUIZ: 2. Refer to the figure. Name the postulate or theorem used in the following statementStatements Reasons

1. <1 ≡ <2 Alternate interior Angles2. <3 ≡ <4 Corresponding Angle3. <1 and <5 are supplementary Same side of the transversal (interior)4. <8 ≡ <9

5. <9 and <10 are supplementary6. <2 ≡ <3

7. <5 and <7 are supplementary 8. m<3 + m<9 = 180º9. <6 ≡ <9

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QUIZ: 2. Refer to the figure. Name the postulate or theorem used in the following statementStatements Reasons

1. <1 ≡ <2 Alternate interior Angles2. <3 ≡ <4 Corresponding Angle3. <1 and <5 are supplementary Same side of the transversal (interior)4. <8 ≡ <9 Alternate Exterior Angles5. <9 and <10 are supplementary6. <2 ≡ <3

7. <5 and <7 are supplementary 8. m<3 + m<9 = 180º9. <6 ≡ <9

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QUIZ: 2. Refer to the figure. Name the postulate or theorem used in the following statementStatements Reasons

1. <1 ≡ <2 Alternate interior Angles2. <3 ≡ <4 Corresponding Angle3. <1 and <5 are supplementary Same side of the transversal (interior)4. <8 ≡ <9 Alternate Exterior Angles5. <9 and <10 are supplementary Same Side of the Transversal (exterior)6. <2 ≡ <3

7. <5 and <7 are supplementary 8. m<3 + m<9 = 180º9. <6 ≡ <9

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QUIZ: 2. Refer to the figure. Name the postulate or theorem used in the following statementStatements Reasons

1. <1 ≡ <2 Alternate interior Angles2. <3 ≡ <4 Corresponding Angle3. <1 and <5 are supplementary Same side of the transversal (interior)4. <8 ≡ <9 Alternate Exterior Angles5. <9 and <10 are supplementary Same Side of the Transversal (exterior)6. <2 ≡ <3 Linear Pairs7. <5 and <7 are supplementary 8. m<3 + m<9 = 180º9. <6 ≡ <9

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QUIZ: 2. Refer to the figure. Name the postulate or theorem used in the following statementStatements Reasons

1. <1 ≡ <2 Alternate interior Angles2. <3 ≡ <4 Corresponding Angle3. <1 and <5 are supplementary Same side of the transversal (interior)4. <8 ≡ <9 Alternate Exterior Angles5. <9 and <10 are supplementary Same Side of the Transversal (exterior)6. <2 ≡ <3 Linear Pairs7. <5 and <7 are supplementary Linear Pairs8. m<3 + m<9 = 180º9. <6 ≡ <9

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QUIZ: 2. Refer to the figure. Name the postulate or theorem used in the following statementStatements Reasons

1. <1 ≡ <2 Alternate interior Angles2. <3 ≡ <4 Corresponding Angle3. <1 and <5 are supplementary Same side of the transversal (interior)4. <8 ≡ <9 Alternate Exterior Angles5. <9 and <10 are supplementary Same Side of the Transversal (exterior)6. <2 ≡ <3 Linear Pairs7. <5 and <7 are supplementary Linear Pairs8. m<3 + m<9 = 180º Definition of Supplementary Angles9. <6 ≡ <9

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QUIZ: 2. Refer to the figure. Name the postulate or theorem used in the following statementStatements Reasons

1. <1 ≡ <2 Alternate interior Angles2. <3 ≡ <4 Corresponding Angle3. <1 and <5 are supplementary Same side of the transversal (interior)4. <8 ≡ <9 Alternate Exterior Angles5. <9 and <10 are supplementary Same Side of the Transversal (exterior)6. <2 ≡ <3 Linear Pairs7. <5 and <7 are supplementary Linear Pairs8. m<3 + m<9 = 180º Definition of Supplementary Angles9. <6 ≡ <9 Alternate Exterior Angles

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