2025 · Standard · Set 5 · Part 3·Q32·5 marks
Triangles
Question
State the basic proportionality theorem. Use the theorem to do the following:
In , AD is the angle bisector of angle A. BA is produced to E such that . Prove that .
Approach
Basic Proportionality Theorem: If a line is drawn parallel to one side of a triangle, it divides the other two sides proportionally. Using the theorem and the given construction with , along with properties of angle bisector, we prove the required ratio.
Step-by-step working
- 1
State BPT
1 mark - 2
Apply to given configuration
2 marks - 3
Use angle bisector properties
1 mark - 4
Conclude
1 mark
Concepts used
basic proportionality theoremangle bisectorparallel linessimilarity
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