2025 · 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 of BPT: If a line divides two sides of a triangle in the same ratio, then it is parallel to the third side. Given D and E are midpoints of AB and AC, so AD/DB = 1 and AE/EC = 1. Since the ratios are equal, by converse of BPT, DE is parallel to BC.
Step-by-step working
- 1
Statement of converse BPT
1 mark - 2
Given, To prove, correct figure
1 mark - 3
D is midpoint of AB AD/DB = 1
1 mark - 4
E is midpoint of AC AE/EC = 1 AD/DB = AE/EC
1 mark - 5
By converse of BPT, DE BC
1 mark
Concepts used
basic proportionality theoremconversemidpoint theoremparallel lines
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