2026 · Basic · 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
State BPT: a line parallel to one side divides the other two sides proportionally. Apply this with the midpoint condition to show the line bisects the third side.
Step-by-step working
- 1
State BPT: If a line is parallel to a side of triangle, it divides the other two sides proportionally
1 mark - 2
Let D be midpoint of AB, and DE BC
1 mark - 3
By BPT:
1.5 marks - 4
Since AD = DB, we get AE = EC, so E bisects AC
1.5 marks
Concepts used
basic proportionality theoremmidpoint theoremparallel lines
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