Difference between revisions of "1991 AHSME Problems/Problem 4"
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| + | == Problem == | ||
| + | |||
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 triangle | (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 == | ||
| + | <math>\fbox{C}</math> | ||
| + | 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 == | ||
| + | {{AHSME box|year=1991|num-b=3|num-a=5}} | ||
| + | |||
| + | [[Category: Introductory Geometry Problems]] | ||
| + | {{MAA Notice}} | ||
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
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 (Problems • Answer Key • Resources) | ||
| 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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
