2025 · Standard · Set 6 · Part 3·Q32·5 marks
Triangles
Question
In the adjoining figure, is a right triangle, right angled at A and . Prove that . Further, if cm and cm, find the length of AD.
Approach
Prove similarity using AA criterion: ∠ADB = ∠CDA = 90° and ∠ABD = ∠CAD (complementary). Then AD²=CD×BD. With BC=10, CD=2, BD=8, so AD²=16, AD=4 cm (using appropriate correction if needed).
Step-by-step working
- 1
Identify right angles and common angles
1 mark - 2
Prove △ADB ~ △CDA by AA similarity
2 marks - 3
Use similarity ratio: AD/CD = BD/AD
1 mark - 4
Compute AD = √(CD×BD) = √(2×8) = 4 cm
1 mark
Concepts used
similar trianglesright triangleperpendicularpythagoras
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