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Parallel and Perpendicular Lines 3
A
B
C
D
E
F
G
H
I
Result
. . . .

Complete the two-column proof. Identify the missing statement. Type the letter of your answer in each blank.

Given:   AS ¯ ∥ IE ¯ and ∠ISE≅∠ISA
Prove:   RI ¯ ∥ SE ¯
Choices:
a. ∠SIA≅∠ISE≅∠ISA≅∠SIE
b. ∠ASE≅∠AIE
c. ∠AIE≅∠RAS
d. m∠ASE=m∠ISA+m∠ISE
e. m∠ASE=m∠ISA+m∠SIA
f. ∠SIA≅∠ISE
g. ∠ASE≅∠RAS
h. m∠ASE=m∠AIE
i. m∠SIA=m∠ISE=m∠ISA=m∠SIE
j. ∠ISE≅∠ISA
k. ∠SIA≅∠ISE and ∠SIE≅∠ISA
l. AS ¯ ∥ IE ¯

Proof:
Statements Reasons
1.
AS ¯ ∥ IE ¯
∠ISE≅∠ISA
1. Given
2.
2. Alternate Interior Angles Theorem
3.
3. Transitive Property of Angle Congruence
4.
4. Definition of congruent angles
5.
m∠AIE=m∠SIA+m∠SIE
5. Angle Addition Postulate
6.
m∠AIE=m∠SIA+m∠ISA
6. Statements 2 and 5, and Substitution Property of Equality
7.
7. Transitive Property of Equality
8.
8. Definition of congruent angles
9.
9. Corresponding Angles Postulate
10.
10. Transitive Property of Angle Congruence
11.
∠ASE and ∠RAS are alternate interior angles.
11. Definition of alternate interior angles
12.
RI ¯ ∥ SE ¯
12. Converse of Alternate Interior Angles Theorem
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