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Which of following indicates that ∆ABC is a right triangle?

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Bunuel
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Which of following indicates that ∆ABC is a right triangle? [#permalink] New post   03 Apr 2019, 23:05
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45% (medium)

Question Stats:

53% (01:23) correct 47% (01:15) wrong based on 53 sessions
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Which of following indicates that ∆ABC is a right triangle?

I. The angles of ∆ABC are in the ratio 1 : 2 : 3.
II. One of the angles of ∆ABC equals the sum of the other two angles.
III. ∆ABC is similar to the right triangle ∆DEF.

(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I, II, and III
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E
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EgmatQuantExpert
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Re: Which of following indicates that ∆ABC is a right triangle? [#permalink] New post   03 Apr 2019, 23:50
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Solution


To find:
    • Among the given statements, which ones indicate ∆ABC is a right triangle.

Approach and Working:
Statement I: The angles of ∆ABC are in the ratio 1: 2: 3.

If we assume the angles to be x, 2x and 3x, then we can say x + 2x + 3x = 180 implies x = 30
    • Therefore, the angles are 30, 60 and 90
    • Hence, ∆ABC is a right triangle

Statement II: One of the angles of ∆ABC equals the sum of the other two angles.

If we assume two angles as a and b, then the third angle should be a + b.
    • Therefore, a + b + a + b = 180 implies a + b = 90, which is the third angle
    • Hence, ∆ABC is a right triangle

Statement III: ∆ABC is similar to the right triangle ∆DEF

As ∆ABC is similar to a right triangle, then they will have the same angles.
    • Hence, ∆ABC is a right triangle

Hence, the correct answer is option E.

Answer: E

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jfranciscocuencag
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Which of following indicates that ∆ABC is a right triangle? [#permalink] New post   29 Apr 2019, 19:14
EgmatQuantExpert wrote:

Solution


To find:
    • Among the given statements, which ones indicate ∆ABC is a right triangle.

Approach and Working:
Statement I: The angles of ∆ABC are in the ratio 1: 2: 3.

If we assume the angles to be x, 2x and 3x, then we can say x + 2x + 3x = 180 implies x = 30
    • Therefore, the angles are 30, 60 and 90
    • Hence, ∆ABC is a right triangle


Statement II: One of the angles of ∆ABC equals the sum of the other two angles.

If we assume two angles as a and b, then the third angle should be a + b.
    • Therefore, a + b + a + b = 180 implies a + b = 90, which is the third angle
    • Hence, ∆ABC is a right triangle

Statement III: ∆ABC is similar to the right triangle ∆DEF

As ∆ABC is similar to a right triangle, then they will have the same angles.
    • Hence, ∆ABC is a right triangle

Hence, the correct answer is option E.

Answer: E



Hello EgmatQuantExpert!!!

Regarding the yellow statement... What if the triangle is an isosceles right triangle? ( 1 : 1 : square root 2)
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Re: Which of following indicates that ∆ABC is a right triangle? [#permalink] New post   30 Apr 2019, 04:41
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Hey jfranciscocuencag,

Can the ratio of angles be 1: 2: 3 if the triangle is an isosceles triangle?

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gmatclubot
Re: Which of following indicates that ∆ABC is a right triangle? [#permalink]
30 Apr 2019, 04:41
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