Saved Bookmarks
| 1. |
Show that the line segments joining the midpoints of theopposite sides of a quadrilateral and bisect each other. |
|
Answer» : ABCD is a quadrilateral P,Q,R&S r the midpoints of the respective sidesTo prove:PR and QS bisect each otherProof: Join PQ,QR,RS,PSJoin diagonals AC and BDIn ΔABC,P and Q r the midpoints of AB and BC respectivelyTherefore by midpoint theorem, PQ is parallel to AC and PQ=1/2ACIn the same way prove that SR is parallel to AC and SR=1/2ACTherefore since the opposite sides are equal and parallel PQRS is a parallelogramIn a parallelogram diagonals bisect each otherHence Proved |
|