2020 · Q65
Consider the following statements:
- 1The diagonals of a trapezium divide each other proportionally.
- 2Any line drawn parallel to the parallel sides of a trapezium divides the non-parallel sides proportionally.
Which of the above statements is/are correct?
Elementary MathematicsQuadrilaterals and Polygons
- A1 only
- B2 only
- CBoth 1 and 2
- DNeither 1 nor 2
Explanation
Both are standard theorems: the diagonals of a trapezium divide each other proportionally (similar triangles), and a line parallel to the parallel sides divides the non-parallel sides proportionally. Both statements are correct - option (C). The first follows from the similar triangles formed by the diagonals; the second is the basic proportionality (Thales) theorem.