Question

In the figure below, find the length of `bar(RS)` if `bar(XY)` is a perpendicular bisector of `bar(TS)` and `TR = "15 cm"`?

Answer 1

`"15 cm"`.

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If `bar(XY)` perpendicularly bisects `bar(TS)`, it is perpendicular, meaning it is at a `90^@` angle to `bar(TS)`, and if it bisects, it divides in two. But if `bar(XY)` bisects `bar(TS)` at a `90^@` angle, then `bar(XY)` is also divided in two.

Therefore, the length of `bar(RS)` is equal to the length of `bar(RX)`, `bar(TR)`, and `bar(RY)`.

As a result, if `bar(TR)` is `"15 cm"` long, then the length of `bar(RS)` is also `"15 cm"`.

CHALLENGE: What about the length of `bar(XY)`? What would that be?