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How to do the steps in the statement and give reasons for the steps

How to do the steps in the statement and give reasons for the steps-example-1
User Mrduclaw
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1 Answer

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19 votes

We have to prove p || q, given r || s and that <1 and <4 are supplementary.

We can start with <4 and <7, that form a linear pair. Then, as <4 and <7 are complementary, then <1 and <7 are congruent.

Then, for <1, formed at the intersection of p and r, to be congruent with <7, formed at the intersection of q and s, then, as r || s, p and q have to be parallel.

We can write as statement - reason pair as:

1) Statement: r || s. Reason: Given.

2) Statement: <1 and <4 are supplementary. Reason: Given.

3) Statement: <4 and <7 are supplementary. Reason: Linear pair.

4) Statement: <1 ≅ <7. Reason: Supplements of the same angle are congruent.

5) Statement: p || q. Reason: As r || s, <1 and <7 are corresponding angles. Then p || q.

User Kai ZHAO
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