Explanation:
It can help to draw your own figure with the right angles better represented. You will notice that right triangles PQR and PRS share side RS. PQ is the hypotenuse of one of them; RS is the hypotenuse of the other.
We can write two equations that make use of the Pythagorean theorem:
PQ² = PR² +RQ²
RS² = QS² +RQ²
Then we can swap sides of the first equation and subtract the second equation. This gives ...
(PR² +RQ²) -(RS²) = (PQ²) -(QS² +RQ²)
Adding RQ², we can write this as ...
PR² -RS² +2RQ² = PQ² -QS²
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The given relationship PR > RS means that PR² -RS² will be positive, so the left side of this equation must be positive.
Since PQ² - QS² is a positive number, PQ > QS.
