Q. Is ABC an equilateral triangle?
1. ∠ABC = ∠ACB
2. Length of AB = Length of AC and one of the angles of the triangle is 60 degrees
OA B
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Q. Is ABC an equilateral triangle?
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BTGmoderatorDC
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Q. Is ABC an equilateral triangle?
1. ∠ABC = ∠ACB
2. Length of AB = Length of AC and one of the angles of the triangle is 60 degrees
OA B
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Ian Stewart
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Statement 1 alone only ensures the triangle is isosceles.
From Statement 2, two sides are equal, so two angles must be equal. We also know one angle is 60 degrees. If that's one of the two equal angles, we have two 60 degree angles, and the third angle then must also be 60 degrees (because a triangle's angles sum to 180 degrees), and our triangle is equilateral. If that 60 degree angle is not one of the two angles we know to be equal, then those two equal angles need to sum to 120, and they are thus both 60 degrees, and again our triangle is equilateral. So Statement 2 is sufficient.
From Statement 2, two sides are equal, so two angles must be equal. We also know one angle is 60 degrees. If that's one of the two equal angles, we have two 60 degree angles, and the third angle then must also be 60 degrees (because a triangle's angles sum to 180 degrees), and our triangle is equilateral. If that 60 degree angle is not one of the two angles we know to be equal, then those two equal angles need to sum to 120, and they are thus both 60 degrees, and again our triangle is equilateral. So Statement 2 is sufficient.
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deloitte247
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Statement 1=> ∠ABC = ∠ACB
There is no specific information about the sides for angles. Hence, statement 1 is INSUFFICIENT.
Statement 2=> Length of AB = Length of AC, and one of the angles of the triangle is 60 degrees.
For a triangle to have 2 equal sides, it means it has 2 equal angles, and with the third angle being 60 degrees.
$$180=60+\frac{120}{2}+\frac{120}{2}$$
$$180=60+60+60$$
Hence, it is an equilateral triangle. Statement 2 alone is SUFFICIENT.
The correct answer is OPTION B
There is no specific information about the sides for angles. Hence, statement 1 is INSUFFICIENT.
Statement 2=> Length of AB = Length of AC, and one of the angles of the triangle is 60 degrees.
For a triangle to have 2 equal sides, it means it has 2 equal angles, and with the third angle being 60 degrees.
$$180=60+\frac{120}{2}+\frac{120}{2}$$
$$180=60+60+60$$
Hence, it is an equilateral triangle. Statement 2 alone is SUFFICIENT.
The correct answer is OPTION B
