Given: r is perpendicular to s, t is perpendicular to s

prove:r is parallel to t

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NOOo

To prove that r is parallel to t using the given information, we can use the concept of transitivity of parallel lines. Here's how you can show this:

1. Given information: r is perpendicular to s and t is perpendicular to s.
- This means that the angle between r and s, as well as the angle between t and s, is 90 degrees.

2. Using the definition of perpendicular lines, we can conclude that the angle between r and t is also 90 degrees.
- This is because if two lines are perpendicular to the same line, they are parallel to each other.

3. Now, let's assume for contradiction that r is not parallel to t.
- If r and t are not parallel, then their corresponding angles would not be 90 degrees.

4. We have a contradictory assumption, as we know that the only line perpendicular to r is s, and the only line perpendicular to t is s.
- This means that the lines r and t are parallel to s, and thus, they must also be parallel to each other.

5. Therefore, we have proved that r is parallel to t using the given information and the concept of transitivity of parallel lines.

In conclusion, by showing that r and t are both perpendicular to s, we can deduce that r is parallel to t.

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