Answer
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Work Step by Step
According to the triangle-angle-bisector theorem, when a ray bisects the angle of a triangle, the opposite side is divided into two segments that are proportional to the remaining two sides of the triangle.
Let's set up a proportion that compares the segments of the intersected side to the other two sides:
$\frac{PT}{TQ} = \frac{KP}{KQ}$
According to a property of proportions, we can switch the means:
$\frac{PT}{KP} = \frac{TQ}{KQ}$
