MHB In the triangle ABC the point D lies on the side BC and point E on the side AB

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In triangle ABC, points D and E are located on sides BC and AB, respectively, with the conditions that BD equals AC, AD equals AE, and AB squared equals the product of AC and BC. The goal is to prove that the angles ∠BAD and ∠CEA are equal. The discussion involves geometric properties and relationships between the sides and angles of the triangle. Participants explore various geometric theorems and relationships to establish the proof. Ultimately, the focus is on demonstrating the angle equality through the given conditions.
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In the triangle ABC the point D lies on the side BC and point E on the side AB. BD = AC, AD = AE and AB ^ 2 = AC * BC. Show that \angle BAD = \angle CEAView attachment 4777
 

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See http://mathhelpboards.com/geometry-11/triangle-prove-16222.html.
 
Thread 'Erroneously finding discrepancy in transpose rule'

Thread 'Erroneously finding discrepancy in transpose rule'

Obviously, there is something elementary I am missing here. To form the transpose of a matrix, one exchanges rows and columns, so the transpose of a scalar, considered as (or isomorphic to) a one-entry matrix, should stay the same, including if the scalar is a complex number. On the other hand, in the isomorphism between the complex plane and the real plane, a complex number a+bi corresponds to a matrix in the real plane; taking the transpose we get which then corresponds to a-bi...
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