¶ 1951 AHSME Problem 29
Problem: Of the following sets of data the only one that does not determine the shape of a triangle is:
Answer Choices:
A. the ratio of two sides and the included angle
B. the ratios of the three altitudes
C. the ratios of the three medians
D. the ratio of the altitude to the corresponding base
E. two angles
Solution:
Let the ratio of altitude to base be . The triangles in the figure satisfy condition (D) but have different shapes. Hence (D) does not determine the shape of a triangle.
