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# Investigation Eight

# Altitudes and Orthocenters

### Chip Meyer

###

### In this investigation, I will look at how ratios from the
orthocenter of a triangle to its points and the feet of the perpendiculars
add up to an interesting number. I need to begin by creating a
triangle ABC

### To find the orthocenter of this triangle, I must now find
the midpoints of each leg of the triangle.

### These midpoints, labeled E, F, and D, now provide me a means
to find the orthocenter as I create perpendiculars from each of
these midpoints. The intersection created by these perpendiculars
will be the orthocenter of my triangle, labeled H.

### The ratios I am trying to discover are shown below. Can these
numbers be found?

### Using the measurement function of the software, I discovered
the following about each segment.

### By using these measurements and creating the ratios I was
interested in, I found the following.

###

### In both cases, the numbers I was trying to find were as I
susupected. However, this these ratios due not work for all triangles.
In the case of an obtuse triangle where the orthocenter is outside
the triangle this does not create the ratios needed to find the
proper answers.