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 Geometry Geometry Math Forum

 April 10th, 2009, 12:07 PM #1 Newbie   Joined: Apr 2009 Posts: 1 Thanks: 0 need help with geometry proof this is kind of a hard question to describe, but ill do my best: let P be any point in the interior of rectangle ABCD (not necessarily the middle). four triangles are formed by joining P to each vertex. demonstrate (prove algebraically) that the area of triangle APD+the area of triangle BPC=the area of triangle APB+the area of triangle PCD. it makes it much easier t o visualize if you draw a simple diagram. thanx for solving this, plz post if you have any questions or need clarification or esp. if you've got the answer!! if you made several diagrams to support your answer, it would be greatly appreciated if you scanned it and sent it to me via email. your help is appreciated April 10th, 2009, 12:29 PM #2 Senior Member   Joined: Mar 2009 Posts: 318 Thanks: 0 Draw the horizontal and vertical lines through P. These lines mark the "height" lines of the four triangles. The pairs of triangles have bases which are on opposite sides of the rectangle. Assuming AB and CD to be the top and bottom of the rectangle, respectively, the triangles APB and CPD have a combined height that is the same as that of the whole rectangle. Obviously, their bases have lengths that are the same as the rectangle's width. So what is their combined area? Consider the same questions for the other pair of triangles. Compare your results.  April 11th, 2009, 09:57 AM #3 Senior Member   Joined: Apr 2009 From: Mesa, Arizona Posts: 161 Thanks: 0 Re: need help with geometry proof Geometry from what I understand is the study of Earth measurement. It is hard to answer yours question algebraically because certain algebra come with it a certain topo. That is, the usage of the word "interior" seems to indicate at least a nature of a topology. For example, at extreme points in considering say R^2, consider point on its boundary, it is uncertain not only in it measurement but also its algebra because it is very much possible that the set of complex number C can literately embeded inside of R. Therefore, because the way it is stated the above and it likes cannot be the case and a geometry must have an equivalence topo represented by an algebra. Locally, geometry is rectangular, this is the use of mathematical quantization. Thus within this quanta, it have bah bah bah; namely, that the area of a triangle is 1/2*b*h. Tags geometry, proof Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Gustav Geometry 6 February 13th, 2018 12:17 AM Gustav Geometry 2 April 14th, 2011 12:26 AM julian21 Geometry 2 September 3rd, 2010 01:05 PM meph1st0pheles Geometry 2 February 9th, 2010 12:32 PM meph1st0pheles Applied Math 1 December 31st, 1969 04:00 PM

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