Difference between revisions of "Symmetry"
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<math>AE = CD = AB \implies \triangle ABE</math> is isosceles. | <math>AE = CD = AB \implies \triangle ABE</math> is isosceles. | ||
− | Therefore < | + | Therefore <cmath>\angle ABC = \angle AEC = \angle ADC \blacksquare.</cmath> |
Revision as of 13:36, 28 August 2023
A proof utilizes symmetry if the steps to prove one thing is identical to those steps of another. For example, to prove that in triangle ABC with all three sides congruent to each other that all three angles are equal, you only need to prove that if then the other cases hold by symmetry because the steps are the same.
Hidden symmetry
Let the convex quadrilateral be given.
Prove that
Proof
Let be bisector
Let point be symmetric with respect
is isosceles.
Therefore