Difference between revisions of "1951 AHSME Problems/Problem 29"
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| + | ==Problem== | ||
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| + | Of the following sets of data, the only one that does not determine the shape of a triangle is: | ||
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| + | <math> \textbf{(A)}\ \text{the ratio of two sides and the inc{}luded angle}\\ \qquad\textbf{(B)}\ \text{the ratios of the three altitudes}\\ \qquad\textbf{(C)}\ \text{the ratios of the three medians}\\ \qquad\textbf{(D)}\ \text{the ratio of the altitude to the corresponding base}\\ \qquad\textbf{(E)}\ \text{two angles} </math> | ||
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| + | ==Solution== | ||
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| + | The answer is <math>\boxed{\textbf{(D)}}</math>. The ratio of the altitude to the base is insufficient to determine the shape of a triangle; you also need to know the ratio of the two segments into which the altitude divides the base. | ||
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== See Also == | == See Also == | ||
{{AHSME 50p box|year=1951|num-b=28|num-a=30}} | {{AHSME 50p box|year=1951|num-b=28|num-a=30}} | ||
Latest revision as of 13:38, 23 September 2024
Problem
Of the following sets of data, the only one that does not determine the shape of a triangle is:
Solution
The answer is 
. The ratio of the altitude to the base is insufficient to determine the shape of a triangle; you also need to know the ratio of the two segments into which the altitude divides the base.
See Also
| 1951 AHSC (Problems • Answer Key • Resources) | ||
| Preceded by Problem 28 |
Followed by Problem 30 | |
| 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 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 • 41 • 42 • 43 • 44 • 45 • 46 • 47 • 48 • 49 • 50 | ||
| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
