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CTK Exchange
Bractals
Member since Jun-9-03
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Jul-25-03, 01:18 PM (EST) |
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"Angle-Side-Side"
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Hi, I recently saw a beautiful proof of the Steiner-Lehmus theorem. But, it used the "Angle-Side-Side (Angle>90)" postulate. On the following site the SSS, SAS, and ASA postulates are shown to be equivalent: Congruences Can anybody give a similar proof for SAS => ASS (A>90) Thanks for the help. Bractals |
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Vladimir
Member since Jun-22-03
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Jul-25-03, 04:31 PM (EST) |
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1. "RE: Angle-Side-Side"
In response to message #0
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LAST EDITED ON Jul-25-03 AT 05:40 PM (EST)
Two triangles DABC and DA'B'C'. Suppose a = a' > 90°, AB = A'B', BC = B'C', and AC ≠ A'C'. If AC < A'C', there is a point E on the ray AC such that AE = A'C' and if AC > A'C', then there is a point D on the ray AC such that AD = A'C'.
Suppose that AC > A'C' and AD = A'C'. Since AD = A'C', a = a', and AB = A'B', DABD = DA'B'C' by SAS. Therefore BD = B'C'. Since BC = B'C' = BD, DCDB is isosceles, and angle CDB = angle DCB < 90°. Consequently, angle ADB > 90° and angle a must be a < 90°. However, this contradicts to a > 90°.
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