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Inside triangle PQR a point O is marked, and D is a point on the segment PO. Through D a line is drawn parallel to OQ meeting PQ at E, and another line is drawn parallel to OR meeting PR at F. What can be said about EF?

Class 10Basic Proportionality TheoremGeometry — Similarity
  • AEF is parallel to PQ, since D lies on PO
  • BNothing follows unless O is the centroid of triangle PQR
  • C is parallel to , since and the converse of BPT then applies
  • DEF is parallel to OD, since DE and DF both start at D

Step-by-Step Solution

Apply BPT twice. In triangle is parallel to , so . In triangle is parallel to OR, so . The common middle ratio gives , and now the converse of BPT in triangle makes parallel to . The position of is irrelevant, so requiring to be the centroid is unnecessary.
Answer: C) is parallel to , since and the converse of BPT then applies

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