1957 AMC 12 Problem 1

Question

The number of distinct lines representing the altitudes, medians, and interior angle bisectors of a triangle that is isosceles, but not equilateral, is:

9

7

6

5

3

Answer: B

Concepts:isosceles triangle median (geometry)altitude angle bisector

Difficulty rating: 1340

Small hint:

Separate the line from the apex from the lines drawn from the two base vertices

Big hint:

At the apex, the altitude, median, and angle bisector coincide; at either base vertex they do not

Solution:

The altitude, median, and angle bisector from the apex are the same line. At each of the two base vertices, those three lines are distinct. Thus there are

1+3+3=7

distinct lines.

Therefore, the correct answer is B.