In triangle MKL, point S lies on side MK, point T on side ML, ST || KL, MT = 4 cm, MS = 5 cm
June 12, 2021 | education
| 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).
One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.