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
State converse of BPT
1 mark - 2
Let D, E be midpoints of AB, AC
1 mark - 31 mark
- 4
By converse BPT,
1 mark - 5
Conclude the proof
1 mark
Concepts used
basic proportionality theoremconversemidpoint theoremproof
Similar question types
- State the converse of "Basic Proportionality Theorem" and use it to prove the following:2025 · Set 1 Part 3 · 5 marks
- State "Basic Proportionality Theorem" and use it to prove the following:2025 · Set 1 Part 2 · 5 marks
- State "Basic Proportionality Theorem" and use it to prove the following: A line through the mid-point of one s…2026 · Set 1 Part 2 · 5 marks
- State "Basic Proportionality Theorem" and use it to prove the following:2025 · Set 1 Part 2 · 5 marks
Stuck on a similar question? Ask the Aethez tutor — it walks you through any Class 10 Maths question step by step.