Re: Geometric Naming

"[Mr.] Lynn Kurtz" <kurtzDELETE-THIS@xxxxxxx> writes in article <HPEiRIIlZl+=0ITcOWp4q1wId2ob@xxxxxxx> dated Thu, 23 Mar 2006 19:11:38 GMT:
On 23 Mar 2006 10:17:17 -0800, liquidfatality@xxxxxxxxx wrote:

Hi, I recently took a test in my geometry class in school. One of the
questions was this:

Given isosceles triangle ABC, such that AB=AC. Draw point D on segment
AC such that, BD=AD=BC. Find the measure of angle A.

After seeing the solution given, angle A=36. However, my arguement is
that I could place point D on segment AC such that D and C are
coinciding. The given restrictions would be met, and I would get the
answer of 60 for angle A.

Is there any rule that says a point cannot be named with two different
variables? Or any other fact that would prove my reasoning wrong?

I'm guessing the problem is worded somewhat differently, since it
isn't always possible to find such a point D. Maybe something like:

You are given an isosceles triangle ABC such that AB = AC. Given that
it is possible to draw point D on segment AC such that BD=AD=BC, find
the measure of angle A.

Personally I would give you partial credit for finding one possible
answer. But the full answer would be A = 36 or 60 degrees. So if your
teacher gives you partial credit, she shouldn't give full credit for
the answer A = 36. Or she could just decide to give both answers full
credit just because.

The answer A = 36 depends on a set of equations which includes angle BCD,
which is undefined if C=D. Since the problem does not rule out this case,
only the set of both answers is worth full credit, IMHO. A = 60 and A = 36
should each be worth half credit.

This problem could have been avoided if the triangle were given to be
isosceles but not equilateral.

--Keith Lewis klewis {at} mitre.org
The above may not (yet) represent the opinions of my employer.
.

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