Finish the two column proof given below to show that p ll q by filling in the blanks.

Statements Reasons

1.r ll s 1. Given

2. <2 `cong` <3 2. _____

3.<1 `cong` <3 3. _____

4._______ 4.______

5. p ll q 5.______

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The lines r and s are parallel. As p is a transversal the alternate interior angles` /_1` and` /_3` are equal.

`/_2 = /_3` : Given

`/_1 = /_3` : alternate interior angles

`/_2 = /_1` : As `/_2 = /_3` and `/_1 = /_3`

p ||q : As the corresponding angles `/_2` and `/_1` are equal.

1. `r || s` 1. Given

2. `/_2 cong /_3` 2. Given (marked in diagram)

3. `/_1 cong /_3` 3. If two parallel lines are cut by a transversal, then alternate interior angles are congruent.

4. `/_1 cong /_2` 4. The transitive property of congruence (or substitution.)

5. `p || q` 5. If two lines are cut by a transversal and corresponding angles are congruent, then the lines are parallel.

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