Converse of basic proportionality theorem
If a line divides two sides of a triangle in the same ratio, then the line is parallel to the third side.
Practice This ConceptMain explanation
Teacher explanation
The converse works backward from ratios to parallelism. If the two sides are divided proportionally, the segment must be parallel to the base.
Example
If AD/DB = AE/EC, then DE ∥ BC.
Simple analogy
Same ratio, same direction.
Common confusion
Students think the line is parallel only after measuring angles. The ratio test itself is enough.
Exam tip
Look for equal ratios on the two sides that are cut by the same line.
Answer writing and exam use
1-mark use
Write the exact meaning of converse of basic proportionality theorem in one clean line.
2-mark use
Define converse of basic proportionality theorem and add one example or condition.
3-mark use
Explain converse of basic proportionality theorem, show the method or example, and mention the common mistake.
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