by RonPurewal Wed Jul 02, 2008 6:49 am
hey -
as the poster above me has indicated, you don't have enough information, unless you're told that the large triangle is also a right triangle. if it is (i.e., angle PYX is a right angle), then all 3 triangles are similar.
since time is at a premium on this test, though, you won't want to muddle through setting up proportions, etc. to solve the triangles. instead, you should just memorize the following 3 equations:
(GY)^2 = (GP)(GX)
(PY)^2 = (PG)(PX)
(XY)^2 = (XG)(XP)
here's the easiest way to get those down (besides raw memorization, of course):
lay the triangle flat on side PX.
pick one of the points on the bottom of the triangle (the points listed in orange in the above equations).
take the one side in the figure that starts at your chosen point and isn't contained in the bottom side of the diagram. (for instance, if you've chosen point G, then this side will be GY.) that side is going to be SQUARED.
take the 2 sides in the bottom of the diagram that start at the orange point. (if you've chosen point G, then these are GP and GX.) those sides are going to be multiplied together.
then set the square and the product equal. voilà !
