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The ratio of the angles in ABC is 2 : 3 : 4. Which one of
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14 Apr 2019, 01:48
14 Apr 2019, 01:48
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The ratio of the angles in \(\triangle ABC\) is 2 : 3 : 4. Which one of the following triangles is similar to \(\triangle\) ABC ?
(A) \(\triangle DEF\) has angles in the ratio 4 : 3 : 2.
(B) \(\triangle PQR\) has angles in the ratio 1 : 2 : 3.
(C) \(\triangle LMN\) has angles in the ratio 1 : 1 : 1.
(D) \(\triangle STW\) has sides in the ratio 1 : 1 : 1.
(E) \(\triangle XYZ\) has sides in the ratio 4 : 3 : 2.
(A) \(\triangle DEF\) has angles in the ratio 4 : 3 : 2.
(B) \(\triangle PQR\) has angles in the ratio 1 : 2 : 3.
(C) \(\triangle LMN\) has angles in the ratio 1 : 1 : 1.
(D) \(\triangle STW\) has sides in the ratio 1 : 1 : 1.
(E) \(\triangle XYZ\) has sides in the ratio 4 : 3 : 2.
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Re: The ratio of the angles in ABC is 2 : 3 : 4. Which one of
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20 Apr 2020, 16:02
20 Apr 2020, 16:02
1
Carcass wrote:
The ratio of the angles in \(\triangle ABC\) is 2 : 3 : 4. Which one of the following triangles is similar to \(\triangle\) ABC ?
(A) \(\triangle DEF\) has angles in the ratio 4 : 3 : 2.
(B) \(\triangle PQR\) has angles in the ratio 1 : 2 : 3.
(C) \(\triangle LMN\) has angles in the ratio 1 : 1 : 1.
(D) \(\triangle STW\) has sides in the ratio 1 : 1 : 1.
(E) \(\triangle XYZ\) has sides in the ratio 4 : 3 : 2.
(A) \(\triangle DEF\) has angles in the ratio 4 : 3 : 2.
(B) \(\triangle PQR\) has angles in the ratio 1 : 2 : 3.
(C) \(\triangle LMN\) has angles in the ratio 1 : 1 : 1.
(D) \(\triangle STW\) has sides in the ratio 1 : 1 : 1.
(E) \(\triangle XYZ\) has sides in the ratio 4 : 3 : 2.
For similar triangle, the angles of the two triangles should be the same. This is clearly valid in Option A
Since the angles are not equal, the side ratio cannot be equal either. Hence, it cannot be D
Also, the ratio of the angles is NOT equal to the ratio of sides (except for equilateral triangles) - for rxample, in a 30-60-90 triangle, the side ratio is not 1 : 2 : 3 . Thus, it is not option E either.
Answer A
gmatclubot
Re: The ratio of the angles in ABC is 2 : 3 : 4. Which one of [#permalink]
20 Apr 2020, 16:02
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