Difference between revisions of "1951 AHSME Problems/Problem 29"
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==Problem== | ==Problem== | ||
| − | Of the following sets of data the only one that does not determine the shape of a triangle is: | + | Of the following sets of data, the only one that does not determine the shape of a triangle is: |
<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> | <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> | ||
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 | |
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| All AHSME Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
