4024/11 Oct/Nov 2022, Question 19: 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
Using the equilateral triangle ABD with C on DB and AC perpendicular to DB, prove that triangles ADC and ABC are congruent, justifying each step.
Summarised in our own words. Use the official paper for the exact wording and the diagram.
Solution · 3 marks
- 1AD = AB (sides of an equilateral triangle)
- 2AC = AC (common side)
- 3Angle ACD = angle ACB = 90° (AC perpendicular to DB)
- 4So triangle ADC is congruent to triangle ABC (RHS)
AnswerAC = AC (common side), AD = AB (equilateral triangle), angle ACD = angle ACB = 90°, congruent (RHS)
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