4024/11 May/Jun 2021, Question 17: Congruent Triangles: Proof Conditions
Cambridge O Level Mathematics 4024 · Paper 11 (Non-calculator) · Non-calculator · 3 marks
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The question, in short
In isosceles triangle ABC with AB = AC, D lies on AC and E on AB, with angle ADB = angle AEC = 90°. Prove triangles ADB and AEC congruent, justifying each step.
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Solution · 3 marks
- 1Angle A is common to both triangles
- 2Angle AEC = angle ADB = 90° (given)
- 3AB = AC (given, triangle ABC is isosceles)
- 4Triangle ADB is congruent to triangle AEC (AAS)
AnswerAngle A is common Angle AEC = angle ADB = 90° (given) AB = AC (given) Triangle ADB is congruent to triangle AEC (AAS)
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