If p is perpendicular to q, q is parallel to r, r is parallel to s, s is perpendicular to t, then which of the following statements is not true?
p is parallel to t
q is perpendicular to t
p is parallel to s
r is perpendicular to p
The statement "r is perpendicular to p" is not true.
The statement "r is perpendicular to p" is not true. According to the given information, p is perpendicular to q, q is parallel to r, and r is parallel to s. But there is no information indicating that r is perpendicular to p.
To determine which statement is not true, we need to analyze the given information step by step and apply the properties of perpendicular and parallel lines.
1. p is perpendicular to q: This means that p and q form a right angle. Therefore, p and q are not parallel.
2. q is parallel to r: This indicates that q and r are parallel lines. Since p is perpendicular to q, it cannot be parallel to r. Thus, the statement "p is parallel to r" is not true.
3. r is parallel to s: This statement tells us that r and s are parallel.
4. s is perpendicular to t: That means s and t form a right angle. Consequently, s and t are not parallel.
To summarize:
- p is not parallel to q.
- r is parallel to s.
- s is not parallel to t.
Now, let's evaluate each given statement based on the analysis above:
a) p is parallel to t: Since s and t are not parallel, and p is perpendicular to q (which is not parallel to r), p cannot be parallel to t. Therefore, this statement is not true.
b) q is perpendicular to t: As stated, s and t are perpendicular. For this reason, q can be perpendicular to t. So, this statement is true.
c) p is parallel to s: As mentioned earlier, p and q are not parallel, and s and t are not parallel either. Hence, this statement is not true.
d) r is perpendicular to p: According to the given information, r and s are parallel, and p and q are perpendicular. Therefore, r cannot be perpendicular to p. Thus, this statement is not true.
The statement that is not true is: a) p is parallel to t.