First let's prove that triangle SKT is congruent to triangle RLT
Angle 3 = angle 4 is given. So is angle 1 = angle 2. Furthermore, we are told that TK = TL. By the ASA theorem, we can show that triangle SKT is congruent to triangle RLT
Then using CPCTC (Corresponding Parts of Congruent Triangles are Congruent), we can prove that ST = TR. We'll use this fact later so keep in mind that ST = TR.
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Let angle 5 be the angle LTK (sandwiched between angle 1 and angle 2). Angle 5 is overlapping between the two triangles RTK and STL.
Since (angle1) = (angle2), we can add the quantity "angle5" to both sides to get
(angle1)+(angle5) = (angle5)+(angle2)
meaning that angle STL = angle RTK
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So we know that ST = TR, which was proven earlier above. We're given TK = TL and finally we found that angle STL = angle RTK. So we can use the SAS property to prove triangle RTK is congruent to triangle STL. That wraps up the proof.