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Suppose triangle is
A
B x z y C
Assume angle AxB is 90, and that angle yAC equals angle yAB and that segment
Bz equals segment zC in length.
I'd describe line Ax by saying
Drop a perpendicular from A to line BC. This Ax line is a height of
the triangle.
I'd describe line Ay as the bisector of the angle BAC. Note that we use the
word "line" here to indicate what Euclidean geometry calls a "line segment",
but in common English, a straight set of points from one point to another is
commonly called a "line", as in "please draw a straight line from A to B".
I'd describe z as the midpoint of segment BC, but I don't know of a common
word for segment Az. I would say "draw a segment from A to the midpoint of
BC".
If you want to pose a construction problem, I might pose it like this:
Given point A, and the three segments, Ax, Ay, and Az, where Ax is the
height of a triangle ABC, and Ay bisects angle BAC, and z is the
midpoint of segment BC, construct points B and C, using only a
straight edge and compass.
/Eric
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| 1. Median to BC
2. Bisector of angle BAC
3. Height (relative to BC as base).
We would understand "build" but most would say "construct".
If the vertices of a triangle are labeled A, B, and C, and
you are given:
AM, the median to BC,
AP, the bisector of <BAC, and
AH, the height above BC,
how would you construct <| ABC?
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