determining from angles that a triangle is isosceles
The following theorem holds in any geometry in which ASA is valid. Specifically, it holds in both Euclidean geometry and hyperbolic geometry (and therefore in neutral geometry) as well as in spherical geometry.
Let triangle have angles and congruent.
Since we have
by the symmetric property (http://planetmath.org/Symmetric) of
we can use ASA to conclude that . Since corresponding parts of congruent triangles are congruent, we have that . It follows that is isosceles. ∎
|Title||determining from angles that a triangle is isosceles|
|Date of creation||2013-03-22 17:12:23|
|Last modified on||2013-03-22 17:12:23|
|Last modified by||Wkbj79 (1863)|