1951 AHSME Problems/Problem 29

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.

1951 AHSC (Problems • Answer Key • Resources)
Preceded by Problem 28	Followed by Problem 30
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1951 AHSME Problems/Problem 29

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