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Proving the Diagonals of a Rectangle Congruent

Date: 12/6/95 at 23:7:37
From: Anonymous
Subject: Geometry (proof on rectangles)

I've looked at this problem and don't know where to begin.  How would 
you prove that the diagonals of a rectangle are congruent?

Date: 1/15/96 at 13:49:22
From: Doctor Ethan
Subject: Re: Geometry (proof on rectangles)

Great question. Here is how I would do it.  It is not the only way, but it will work.

Start with a drawing.

|                     |
|                     |
|                     |
|                     |
B                      C

We want to look at the lines AC and BD.

To do this I want you to imagine two triangles, ABC  and DBC.
I am going to pull them apart, and they will look like this:

A                                                     D
|                                                     |
|                                                     |
|                                                     |
|______________________       ________________________|
B                      C      B                       C

Now, do you know the SAS triangle congruency postulate?

If you do then you will recognize that DC is congruent to AB, 
BC is congruent to BC, and Angle A is congruent to Angle C.

Triangle ABC is congruent to Triangle DCB, so AC is congruent to DB.
That is what we wanted to prove.

Hope that helps.

- Doctor Ethan,  The Geometry Forum

Associated Topics:
High School Geometry
High School Triangles and Other Polygons

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