Proving the Diagonals of a Rectangle CongruentDate: 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. A_____________________D | | | | | | | | |_____________________| 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 |
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