Question

Consider the diagram.


Which line segment has the same measure as ST?

Answer 1

SR because any point on a perpendicular bisecting line is equidistant from the ends of the bisected segment.

Answer 2

`SR`

Explanation:

In this problem we have

`RX=XT` -----> given problem

`XS` ---> is a common side both triangles

In the right triangle RSX

Applying the Pythagoras Theorem

`SR^(2)=RX^(2)+XS^(2)` ------> equation A

In the right triangle XST

Applying the Pythagoras Theorem

`ST^(2)=XT^(2)+XS^(2)` ------> equation B

remember that ----->
`RX=XT`

Substitute

`ST^(2)=RX^(2)+XS^(2)` ------> equation C

Compare equation A and equation C

`SR=ST`