- This topic has 1 reply, 2 voices, and was last updated 10 years, 7 months ago by
.
-
Posts
-
GPE-4 states that students should be able to, “Use coordinates to prove simple geometric theorems algebraically.” Upon first read, this standard seems pretty straightforward. I imagine students using the coordinate plane setting to prove statements such as, “The diagonals of a rectangle are congruent” or “The diagonals of a parallelogram bisect each other” or “The mid-segment of a triangle is parallel to a side of the triangle.” But what follows threw me for a loop:
For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2).
These examples do not describe what I would have considered a proof of a geometric theorem. The types of problems described in the example certainly have pedagogical merit; they simply do not describe what I would consider geometric theorems. Can you help me reconcile these examples with the statement of the standard?
There is that word “simple” in there. The examples are not intended to be exhaustive, of course, but they do illustrate what is meant by that word. I would say that the examples you gave, while certainly falling within the meaning of the standard, are not required by it. Such theorems should certainly be proved, but proofs using congruence and similarity make more sense to me. The analytic proofs would be quite laborious, wouldn’t they?
- You must be logged in to reply to this topic.