In the trapezoid PQRS with bases QR and PS, the diagonals meet at point K. a) Prove the similarity of the triangles

| August 28, 2021 | education

In the trapezoid PQRS with bases QR and PS, the diagonals meet at point K. a) Prove the similarity of the triangles QRK and SPK. b) Find the lengths of the segments KQ and KS, if QR = 5m, SP = 15m, QS = 12.8m.

a) Triangles SPK and QRK are similar, since their bases lie on the lower and upper bases of the trapezoid, respectively. The angles QRK and RPS are formed by the bases and a common straight line – the diagonal. Therefore, these angles are equal. The corners RQK and KSP are also formed by the bases and a common line – another diagonal. Therefore, these angles are also equal to each other.
The angles QKR and PKS are equal to each other, since they are formed by two segments – diagonals.
All angles are respectively equal – the similarity is proven.



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.