1951 AHSME Problems/Problem 29

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Problem

Of the following sets of data the only one that does not determine the shape of a triangle is:

$\textbf{(A)}\ \text{the ratio of two sides and the inc{}luded angle}\\ \qquad\textbf{(B)}\ \text{the ratios of the three altitudes}\\ \qquad\textbf{(C)}\ \text{the ratios of the three medians}\\ \qquad\textbf{(D)}\ \text{the ratio of the altitude to the corresponding base}\\ \qquad\textbf{(E)}\ \text{two angles}$

Solution

The answer is $\boxed{\textbf{(D)}}$. 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 (ProblemsAnswer KeyResources)
Preceded by
Problem 28
Followed by
Problem 30
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