Short Answer 
The answer explains that line segments ST and UT are congruent because they are tangents to the same circle, creating right angles with the radii at points S and U. By applying the Hypotenuse-Leg (HL) Postulate, it is established that both segments are equal in length.
Step 1: Identify Tangents and Radii
In the given figure, line segments ST and UT are declared as tangents to circle K at points S and U respectively. Since these lines touch the circle only at one point, they are perpendicular to the radii at those points. This means:
- Line segment KS is a radius meeting tangent ST at point S.
- Line segment KU is a radius meeting tangent UT at point U.
Step 2: Establish Right Angles
Since the tangents are perpendicular to the radii at the points of tangency, we can conclude that the angles formed are right angles. Specifically, the angles are:
- ‚Äöa‚ĆKST = 90¬¨‚à û at point S
- ‚Äöa‚ĆKUT = 90¬¨‚à û at point U
With both angles being equal, we can further establish that the triangles KST and KUT share the same angle measure at K.
Step 3: Apply the HL Postulate for Congruence
In triangles KST and KUT, we have identified the components needed for the Hypotenuse-Leg (HL) Postulate of congruence. These components include:
- KS = KU (both are radii of the same circle).
- KT is the common hypotenuse for both triangles.
Since both triangles KST and KUT have congruency through the HL postulate, we can conclude that ST is congruent to UT, resulting in the statement: Line segment ST is congruent to line segment UT.