Angle-Side-Side Does Not WorkDate: 11/12/2001 at 11:18:12 From: Dana Hess Subject: Angle-Side-Side does not prove 2 triangles congruent? Can you give me a construction to show that Angle-Side-Side does not prove two triangles congruent? I would like to show my students why it does not work, and for some reason I keep coming up with two congruent triangles when I am done. It would be great if they could even do this on the Geometer's Sketchpad to see that SSS, ASA, SAS, and AAS work, but AAA and SSA do not. Thank you! Dana Date: 11/12/2001 at 11:37:33 From: Doctor Mitteldorf Subject: Re: Angle-Side-Side does not prove 2 triangles congruent? Dana - For most combinations, there is only one triangle that can be drawn from an angle-side-side specification. But here's an example of the ambiguous case: Specify angle = 30, adjacent side = sqrt(3), opposite side = 1. Draw two triangles: - one with the angles 30-30-120 and the sides 1,1,sqrt(3) - the other with angles 30-90-60 and sides 1,2,sqrt(3) - Doctor Mitteldorf, The Math Forum http://mathforum.org/dr.math/ |
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