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16 Sep 2014, 00:15
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Is triangle ABC above an isosceles triangle?
(1) Angle ACB is twice as large as angle ADC.
(2) Angle ACB is twice as large as angle CAB.
16 Sep 2014, 00:15
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Official Solution:
Is triangle ABC above an isosceles triangle?
Since triangle ABC is a right triangle, we need to determine if angle ACB is equal to angle CAB. If these angles are equal, then side AB would be equal to side BC, making triangle ABC an isosceles triangle.
(1) Angle ACB is twice as large as angle ADC.
It's possible for angle ACB to be equal to angle CAB (45 degrees) with angle ADC at 22.5 degrees:
However, it's also possible for angle ACB NOT to be equal to angle CAB, for example, if angle ACB is 60 degrees and angle ADC is 30 degrees:
Not sufficient.
(2) Angle ACB is twice as large as angle CAB.
This statement directly implies that angle ACB is NOT equal to angle CAB. Therefore, triangle ABC is NOT an isosceles triangle. Sufficient.
Answer: B
Is triangle ABC above an isosceles triangle?
Since triangle ABC is a right triangle, we need to determine if angle ACB is equal to angle CAB. If these angles are equal, then side AB would be equal to side BC, making triangle ABC an isosceles triangle.
(1) Angle ACB is twice as large as angle ADC.
It's possible for angle ACB to be equal to angle CAB (45 degrees) with angle ADC at 22.5 degrees:
However, it's also possible for angle ACB NOT to be equal to angle CAB, for example, if angle ACB is 60 degrees and angle ADC is 30 degrees:
Not sufficient.
(2) Angle ACB is twice as large as angle CAB.
This statement directly implies that angle ACB is NOT equal to angle CAB. Therefore, triangle ABC is NOT an isosceles triangle. Sufficient.
Answer: B
General Discussion
