2. GIVEN: P║Q TRANSVERSAL ℓ CUTS
P AND Q
Prove: <1 ≡ <2
Write the corresponding postulates as reasons:
Statements Reasons
1. p║q
2. <3 ≡ <2
3. <1 ≡ <3
4. <1 ≡ <2
1
3
2
3. GIVEN: P║Q TRANSVERSAL ℓ CUTS
P AND Q
Prove: <1 ≡ <2
Write the corresponding postulates as reasons:
Statements Reasons
1. p║q Given
2. <3 ≡ <2
3. <1 ≡ <3
4. <1 ≡ <2
1
3
2
4. GIVEN: P║Q TRANSVERSAL ℓ CUTS
P AND Q
Prove: <1 ≡ <2
Write the corresponding postulates as reasons:
Statements Reasons
1. p║q Given
2. <3 ≡ <2 Corresponding Angle Postulate
3. <1 ≡ <3
4. <1 ≡ <2
1
3
2
5. GIVEN: P║Q TRANSVERSAL ℓ CUTS
P AND Q
Prove: <1 ≡ <2
Write the corresponding postulates as reasons:
Statements Reasons
1. p║q Given
2. <3 ≡ <2 Corresponding Angle Postulate
3. <1 ≡ <3 Vertical Angles Postulate
4. <1 ≡ <2
1
3
2
6. GIVEN: P║Q TRANSVERSAL ℓ CUTS
P AND Q
Prove: <1 ≡ <2
Write the corresponding postulates as reasons:
Statements Reasons
1. p║q Given
2. <3 ≡ <2 Corresponding Angle Postulate
3. <1 ≡ <3 Vertical Angles Postulate
4. <1 ≡ <2 Transitive Property
1
3
2
7. GIVEN: P║Q TRANSVERSAL ℓ CUTS
P AND Q
Prove: <1 and <2 are supplementary
Write the corresponding postulates as reasons:
Statements Reasons
1. p║q Given
2. <2 and <3 are supplementary Linear Pair
3. <1 ≡ <3 Alternate Interior Angle
4. <1 and <2 are supplementary Linear Pair
1
32
8. LET’S TRY
Letter A, page 307. In the given figure, name the postulate or
theorem that justifies each statement, given m ║ n.
9. Statements Reasons
1. <2 ≡ <8
2. <3 ≡ <7
3. <1 ≡ <3
4. <3 and <8 are supplementary
5. <1 ≡ <7
6. <4 and <7 are supplementary
7. There exists a line through P
parallel to line n
8. a ┴b
1
32
10. Statements Reasons
1. <2 ≡ <8 Alternate interior angles
2. <3 ≡ <7
3. <1 ≡ <3
4. <3 and <8 are supplementary
5. <1 ≡ <7
6. <4 and <7 are supplementary
7. There exists a line through P
parallel to line n
8. a ┴b
1
32
11. Statements Reasons
1. <2 ≡ <8 Alternate interior angles
2. <3 ≡ <7 Corresponding angle postulate
3. <1 ≡ <3
4. <3 and <8 are supplementary
5. <1 ≡ <7
6. <4 and <7 are supplementary
7. There exists a line through P
parallel to line n
8. a ┴b
1
32
12. Statements Reasons
1. <2 ≡ <8 Alternate interior angles
2. <3 ≡ <7 Corresponding angle postulate
3. <1 ≡ <3 Vertical Angles Postulate
4. <3 and <8 are supplementary
5. <1 ≡ <7
6. <4 and <7 are supplementary
7. There exists a line through P
parallel to line n
8. a ┴b
1
32
13. Statements Reasons
1. <2 ≡ <8 Alternate interior angles
2. <3 ≡ <7 Corresponding angle postulate
3. <1 ≡ <3 Vertical Angles Postulate
4. <3 and <8 are supplementary Same Side of the transversal are
supplementary
5. <1 ≡ <7
6. <4 and <7 are supplementary
7. There exists a line through P parallel to
line n
8. a ┴b
1
32
14. Statements Reasons
1. <2 ≡ <8 Alternate interior angles
2. <3 ≡ <7 Corresponding angle postulate
3. <1 ≡ <3 Vertical Angles Postulate
4. <3 and <8 are supplementary Same Side of the transversal are
supplementary
5. <1 ≡ <7 Alternate Exterior Angles
6. <4 and <7 are supplementary
7. There exists a line through P parallel to
line n
8. a ┴b
1
32
15. Statements Reasons
1. <2 ≡ <8 Alternate interior angles
2. <3 ≡ <7 Corresponding angle postulate
3. <1 ≡ <3 Vertical Angles Postulate
4. <3 and <8 are supplementary Same Side of the transversal are
supplementary
5. <1 ≡ <7 Alternate Exterior Angles
6. <4 and <7 are supplementary Same Side of the transversal are
supplementary
7. There exists a line through P parallel to
line n
8. a ┴b
1
32
16. Statements Reasons
1. <2 ≡ <8 Alternate interior angles
2. <3 ≡ <7 Corresponding angle postulate
3. <1 ≡ <3 Vertical Angles Postulate
4. <3 and <8 are supplementary Same Side of the transversal are
supplementary
5. <1 ≡ <7 Alternate Exterior Angles
6. <4 and <7 are supplementary Same Side of the transversal are
supplementary
7. There exists a line through P parallel to
line n
Parallel Postulate
8. a ┴b
1
32
17. Statements Reasons
1. <2 ≡ <8 Alternate interior angles
2. <3 ≡ <7 Corresponding angle postulate
3. <1 ≡ <3 Vertical Angles Postulate
4. <3 and <8 are supplementary Same Side of the transversal are
supplementary
5. <1 ≡ <7 Alternate Exterior Angles
6. <4 and <7 are supplementary Same Side of the transversal are
supplementary
7. There exists a line through P parallel to
line n
Parallel Postulate
8. a ┴b Perpendicular Transversal Theorem
1
32
20. 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 supplementary
4. <8 ≡ <9
5. <9 and <10 are supplementary
6. <2 ≡ <3
7. <5 and <7 are supplementary
8. m<3 + m<9 = 180º
9. <6 ≡ <9
3
18
2 9
54 7
1
0
6
25. QUIZ:
1. Given: r║p prove <2 ≡ <3
Statements Reasons
1. r ║ s Given
2. <2 ≡ <1 Vertical Angles
3. <1 ≡ <3 Same Side of the Transversal
4. <2 ≡ <3
1
2
3
26. QUIZ:
1. Given: r║p prove <2 ≡ <3
Statements Reasons
1. r ║ s Given
2. <2 ≡ <1 Vertical Angles
3. <1 ≡ <3 Same Side of the Transversal
4. <2 ≡ <3 Transitive Property
1
2
3
27. 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 supplementary
4. <8 ≡ <9
5. <9 and <10 are supplementary
6. <2 ≡ <3
7. <5 and <7 are supplementary
8. m<3 + m<9 = 180º
9. <6 ≡ <9
3
18
2 9
54 7
1
0
6
28. QUIZ:
2. Refer to the figure. Name the postulate or theorem used in the
following statementStatements Reasons
1. <1 ≡ <2 Alternate interior Angles
2. <3 ≡ <4
3. <1 and <5 are supplementary
4. <8 ≡ <9
5. <9 and <10 are supplementary
6. <2 ≡ <3
7. <5 and <7 are supplementary
8. m<3 + m<9 = 180º
9. <6 ≡ <9
3
18
2 9
54 7
1
0
6
29. QUIZ:
2. Refer to the figure. Name the postulate or theorem used in the
following statementStatements Reasons
1. <1 ≡ <2 Alternate interior Angles
2. <3 ≡ <4 Corresponding Angle
3. <1 and <5 are supplementary
4. <8 ≡ <9
5. <9 and <10 are supplementary
6. <2 ≡ <3
7. <5 and <7 are supplementary
8. m<3 + m<9 = 180º
9. <6 ≡ <9
3
18
2 9
54 7
1
0
6
30. QUIZ:
2. Refer to the figure. Name the postulate or theorem used in the
following statementStatements Reasons
1. <1 ≡ <2 Alternate interior Angles
2. <3 ≡ <4 Corresponding Angle
3. <1 and <5 are supplementary Same side of the transversal (interior)
4. <8 ≡ <9
5. <9 and <10 are supplementary
6. <2 ≡ <3
7. <5 and <7 are supplementary
8. m<3 + m<9 = 180º
9. <6 ≡ <9
3
18
2 9
54 7
1
0
6
31. QUIZ:
2. Refer to the figure. Name the postulate or theorem used in the
following statementStatements Reasons
1. <1 ≡ <2 Alternate interior Angles
2. <3 ≡ <4 Corresponding Angle
3. <1 and <5 are supplementary Same side of the transversal (interior)
4. <8 ≡ <9 Alternate Exterior Angles
5. <9 and <10 are supplementary
6. <2 ≡ <3
7. <5 and <7 are supplementary
8. m<3 + m<9 = 180º
9. <6 ≡ <9
3
18
2 9
54 7
1
0
6
32. QUIZ:
2. Refer to the figure. Name the postulate or theorem used in the
following statementStatements Reasons
1. <1 ≡ <2 Alternate interior Angles
2. <3 ≡ <4 Corresponding Angle
3. <1 and <5 are supplementary Same side of the transversal (interior)
4. <8 ≡ <9 Alternate Exterior Angles
5. <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 = 180º
9. <6 ≡ <9
3
18
2 9
54 7
1
0
6
33. QUIZ:
2. Refer to the figure. Name the postulate or theorem used in the
following statementStatements Reasons
1. <1 ≡ <2 Alternate interior Angles
2. <3 ≡ <4 Corresponding Angle
3. <1 and <5 are supplementary Same side of the transversal (interior)
4. <8 ≡ <9 Alternate Exterior Angles
5. <9 and <10 are supplementary Same Side of the Transversal (exterior)
6. <2 ≡ <3 Linear Pairs
7. <5 and <7 are supplementary
8. m<3 + m<9 = 180º
9. <6 ≡ <9
3
18
2 9
54 7
1
0
6
34. QUIZ:
2. Refer to the figure. Name the postulate or theorem used in the
following statementStatements Reasons
1. <1 ≡ <2 Alternate interior Angles
2. <3 ≡ <4 Corresponding Angle
3. <1 and <5 are supplementary Same side of the transversal (interior)
4. <8 ≡ <9 Alternate Exterior Angles
5. <9 and <10 are supplementary Same Side of the Transversal (exterior)
6. <2 ≡ <3 Linear Pairs
7. <5 and <7 are supplementary Linear Pairs
8. m<3 + m<9 = 180º
9. <6 ≡ <9
3
18
2 9
54 7
1
0
6
35. QUIZ:
2. Refer to the figure. Name the postulate or theorem used in the
following statementStatements Reasons
1. <1 ≡ <2 Alternate interior Angles
2. <3 ≡ <4 Corresponding Angle
3. <1 and <5 are supplementary Same side of the transversal (interior)
4. <8 ≡ <9 Alternate Exterior Angles
5. <9 and <10 are supplementary Same Side of the Transversal (exterior)
6. <2 ≡ <3 Linear Pairs
7. <5 and <7 are supplementary Linear Pairs
8. m<3 + m<9 = 180º Definition of Supplementary Angles
9. <6 ≡ <9
3
18
2 9
54 7
1
0
6
36. QUIZ:
2. Refer to the figure. Name the postulate or theorem used in the
following statementStatements Reasons
1. <1 ≡ <2 Alternate interior Angles
2. <3 ≡ <4 Corresponding Angle
3. <1 and <5 are supplementary Same side of the transversal (interior)
4. <8 ≡ <9 Alternate Exterior Angles
5. <9 and <10 are supplementary Same Side of the Transversal (exterior)
6. <2 ≡ <3 Linear Pairs
7. <5 and <7 are supplementary Linear Pairs
8. m<3 + m<9 = 180º Definition of Supplementary Angles
9. <6 ≡ <9 Alternate Exterior Angles
3
18
2 9
54 7
1
0
6