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Difference between revisions of "1991 AHSME Problems/Problem 4"

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Which of the following triangles cannot exist?
 
Which of the following triangles cannot exist?
  
(A) An acute isosceles triangle (B) An isosceles right triangle (C) An obtuse right triangle (D) A scalene right triangle (E) A scalene obtuse tr
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(A) An acute isosceles triangle (B) An isosceles right triangle (C) An obtuse right triangle (D) A scalene right triangle (E) A scalene obtuse triangle
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== Solution ==
 
== Solution ==

Latest revision as of 04:47, 24 February 2018

Problem

Which of the following triangles cannot exist?

(A) An acute isosceles triangle (B) An isosceles right triangle (C) An obtuse right triangle (D) A scalene right triangle (E) A scalene obtuse triangle

Solution

$\fbox{C}$ A right triangle has an angle of 90 degrees, so any obtuse angle would make the sum of those two angles over 180. This contradicts the angle sum theorem (all triangles have angles that sum to 180) since negative angles don't exist.

See also

1991 AHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 3
Followed by
Problem 5
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
All AHSME Problems and Solutions

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