2025 · Standard · Set 1 · Part 2·Q32·5 marks
Triangles
Question
State "Basic Proportionality Theorem" and use it to prove the following:
A line through the mid-point of one side of a triangle, parallel to another side, bisects the third side.
Approach
Basic Proportionality Theorem: If a line parallel to one side of a triangle intersects the other two sides, it divides them proportionally. Given P is mid-point of AB and PQ parallel to BC. By BPT, AP/PB = AQ/QC. Since AP=PB, we get AQ=QC, so Q is mid-point of AC.
Step-by-step working
- 1
State theorem correctly
1 mark - 2
Given, To prove, Figure (correct)
1 mark - 3
By BPT:
1 mark - 4
AP = PB (given)
1 mark - 5
AQ = QC Q is mid-point
1 mark
Concepts used
basic proportionality theoremproofmid-pointparallel lines
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