Question

The corners and mid-points of the sides of a triangle are named using the distinct letters P, Q, R, S, T, and U, but not necessarily in the same order. Consider the following statements:


The line joining P and R is parallel to the line joining Q and S.
P is placed on the side opposite to the corner T.
S and U cannot be placed on the same side.
Which one of the following statements is correct based on the above information?

• A. P cannot be placed at a corner
• B. S cannot be placed at a corner
• C. U cannot be placed at a mid-point
• D. R cannot be placed at a corner

Hint:

When analyzing geometric placement problems, pay close attention to parallelism, placement restrictions, and the geometric relationships between points and sides.

Answer 1

The Correct Option is B

To solve this problem, let's analyze the information given and the implications:

1. The line joining P and R is parallel to the line joining Q and S.
2. P is placed on the side opposite to the corner T. This indicates that P is at the midpoint of one side of the triangle.
3. S and U cannot be placed on the same side.

We need to determine which placements are not possible for S or U, based on the given conditions:

• When two points (like P and R) have a line that is parallel to another line (like Q and S), both pairs of points are typically at midpoints of opposite sides of the triangle.
• Since P is on the midpoint and cannot be on a corner, S should ideally be placed on a side but not concurrently at a midpoint with U. Since S and U cannot share the same side and midpoints tend to be strategic for these lines, S cannot be effectively positioned at a corner.

Thus, based on the analysis above, the correct statement is: S cannot be placed at a corner.