4024/12 Oct/Nov 2021, Question 12: Similar Triangles
Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 3 marks
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The question, in short
Using the rectangle ABCD with E on diagonal AC and angle DEC = 90°, prove triangle ADC is similar to triangle DEC, justifying each statement.
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Solution · 3 marks
- 1Angle ACD = angle DCE (common/shared angle at C)
- 2Angle ADC = angle DEC = 90° (ADC is an angle of the rectangle, DEC given)
- 3Angle DAC = angle EDC (third angles in a triangle, since angles add to 180°)
- 4All three pairs of angles are equal, so triangle ADC is similar to triangle DEC
Answerangle ACD = angle DCE, shared angle; angle ADC = angle DEC = 90°, given; angle DAC = angle EDC, third angles in a triangle; three angles equal, therefore the triangles are similar
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