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The letters P, Q, R, S, T and U are to be placed one per vertex on a regular convex hexagon, but not necessarily in the same order. Consider the following statements: The line segment joining R and S is longer than the line segment joining P and Q. The line segment joining R and S is perpendicular to the line segment joining P and Q. The line segment joining R and U is parallel to the line segment joining T and Q. Based on the above statements, which one of the following options is CORRECT?

The letters P, Q, R, S, T and U are to be placed one per vertex on a regular convex hexagon, but not necessarily in the same order. Consider the following statements: The line segment joining R and S is longer than the line segment joining P and Q. The line segment joining R and S is perpendicular to the line segment joining P and Q. The line segment joining R and U is parallel to the line segment joining T and Q. Based on the above statements, which one of the following options is CORRECT? Correct Answer The line segment joining R and T is parallel to the line segment joining Q and S

Given:

There is a regular convex hexagon in which the letters P, Q, R, S, T, and U are to be placed one per vertex but not necessarily in the same order.

Concept used:

We have to draw the diagram according to the question to find the correct answer from the given options.

Calculation:

According to the question by using given statements, the regular convex hexagon will be like,

[ alt="F1 Shraddha Engineering 29.03.2022 D3" src="//storage.googleapis.com/tb-img/production/22/03/F1_Shraddha_Engineering_29.03.2022_D3.png" style="height: 132px; width: 233px;">

From the above diagram, we can easily see that the line segment joining R and T is parallel to the line segment joining Q and S.

Hence, option 1 is correct answer. The line segment joining R and T is parallel to the line segment joining Q and S.

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