If pi’s perpendicular to q, q is parallel to r, r is parallel to s, sis perpendicular to t then which of the following statements is not true?
If pi is perpendicular to q, it means that pi forms a right angle with q. Similarly, if si is perpendicular to t, it means that si forms a right angle with t.
If q is parallel to r and r is parallel to s, it implies that q, r, and s are all parallel lines. This means that q, r, and s never intersect and they have the same slope.
Based on the given information, we know that pi forms a right angle with q, q is parallel to r, r is parallel to s, and si forms a right angle with t.
Given this information, we can conclude that si and t are also parallel lines. This is because si is perpendicular to t, which means that si forms a right angle with t. Since si and t have a right angle and r is parallel to s, it implies that si is also parallel to r and, consequently, t is parallel to r.
Therefore, all the statements are true based on the given information, and none of them is not true.
If pi is perpendicular to q, it means that pi forms a right angle with q.
If q is parallel to r, it means that q and r never intersect and their direction remains constant.
If r is parallel to s, it means that r and s never intersect and their direction remains constant.
If si is perpendicular to t, it means that si forms a right angle with t.
Based on the given information, the only statement that is not true is that "pi is perpendicular to q". This is because pi and q are not mentioned to be perpendicular to each other in the given information.
To determine which statement is not true, let's analyze the given information step by step:
1. If pi is perpendicular to q, it means that π and q form a right angle.
2. If q is parallel to r, it means that q and r do not intersect and have the same direction.
3. If r is parallel to s, it means that r and s do not intersect and have the same direction.
4. If s is perpendicular to t, it means that s and t form a right angle.
Now, let's consider the given options and check if they are consistent with the information:
A. r is perpendicular to q.
This statement contradicts the given information because q is perpendicular to π, not r. Therefore, option A is not true.
B. t is parallel to q.
This statement is consistent with the information because t is perpendicular to s, and s is parallel to r, which means that q and t also share the same direction. Therefore, option B is true.
C. π is perpendicular to t.
This statement is consistent with the information because q is perpendicular to π, and q is parallel to r. Since r is parallel to s and s is perpendicular to t, it implies that π is also perpendicular to t. Therefore, option C is true.
D. s is parallel to π.
This statement contradicts the given information because π is perpendicular to q, and q is parallel to r. Since r is parallel to s, s cannot be parallel to π. Therefore, option D is not true.
So, the statement that is not true is option D: "s is parallel to π."