example related to converse of Basic Proportionality Theorem or Thales Theorem
Example 1 . In a figure,PS/SQ =PT/TR and ∠PST = ∠PRQ. prove that PQR is an isosceles triangle. Solution :- it is given that PS/SQ =PT/TR so, ST∥QR ( converse of Basic Proportionality Theorem ) Therefore, ∠PST = ∠PQR (corresponding angles)........(1) Also, it is given that ∠PST =∠PRQ...............(2) so, ∠ PRQ= ∠PQR [ from (1) and (2)] Therefore, PQ = PR (sides opposite the equal angles) i . e. , PQR is an isosceles triangle.