1959 AMC 12 Problem 3
Attempt Problem 3 of the 1959 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1959 AMC 12 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
3.
If the diagonals of a quadrilateral are perpendicular to each other, the figure would always be included under the general classification:
rhombus
rectangle
square
isosceles trapezoid
none of these
Answer: E
Small hint:
Look for a quadrilateral with perpendicular diagonals that is not one of the four named special types
Big hint:
A general kite supplies a useful counterexample
Solution:
A kite can have perpendicular diagonals without being a rhombus, rectangle, square, or isosceles trapezoid. Therefore perpendicular diagonals alone do not force any of the first four classifications.
Thus, the correct answer is E.
Problem 3 in other years
- 1950 AMC 12
- 1951 AMC 12
- 1952 AMC 12
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- 1954 AMC 12
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