shankar.ashwin wrote: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
With I,II,III problems, BE EFFICIENT.
Scan the options and look for the easiest to evaluate.
Eliminate answer choices as you proceed.
Statement III:
No math is necessary. By definition, SIMILAR triangles contain the same combination of angles. Thus, if ∆ABC is similar to the right triangle ∆DEF, then ∆ABC must also be a right triangle.
Eliminate answers that don't include III.
Eliminate A, B and D.
Statement I:
Since the sum of the angles must be 180, and 1:2:3 = 30:60:90 -- yielding a sum of 30+60+90=180 -- ∆ABC is a right triangle whose angles are 30,60, and 90.
Eliminate any remaining answers that don't include I.
Eliminate C.
The correct answer is
E.
No need to evaluate II, a nice time-saver.
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