2026 · Basic · Set 1 · Part 3·Q34·5 marks

Triangles

Question

State the converse of "Basic Proportionality Theorem" and use it to prove the following:
Line segment joining mid-points of any two sides of a triangle is parallel to the third side.

Approach

Converse: If a line divides two sides of a triangle in the same ratio, it is parallel to the third side. Using this, if D and E are midpoints of AB and AC, then , so by the converse, .

Step-by-step working

  1. 1

    State converse of BPT

    1 mark
  2. 2

    Let D, E be midpoints of AB, AC

    1 mark
  3. 3

    1 mark
  4. 4

    By converse BPT,

    1 mark
  5. 5

    Conclude the proof

    1 mark

Concepts used

basic proportionality theoremconversemidpoint theoremproof

Similar question types

Stuck on a similar question? Ask the Aethez tutor — it walks you through any Class 10 Maths question step by step.