In triangle MKL, point S lies on side MK, point T on side ML, ST || KL, MT = 4 cm, MS = 5 cm

In triangle MKL, point S lies on side MK, point T on side ML, ST || KL, MT = 4 cm, MS = 5 cm, TL = 2 cm. Find the length of the segment SK.

Since ST is parallel to KL, angle MKL = angle MST, angle MLK = angle MTS.

Therefore, triangles MST and MKL are similar from the equality of three angles.

Then by the property of similar triangles

MK / MS = ML / MT.

(MS + SK) / MS = (MT + TL) / MT.

(5 + SK) / 5 = (4 + 2) / 4.

4 * (5 + SK) = 30.

4 * SK = 10.

SK = 2.5 (cm).