angles of an isosceles triangle
The following theorem holds in any geometry in which SAS 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 be isosceles such that the legs and are congruent.
Since we have
we can use SAS to conclude that . Since corresponding parts of congruent triangles are congruent, it follows that . ∎
In geometries in which SAS and ASA are both valid, the converse theorem of this theorem is also true. This theorem is stated and proven in the entry determining from angles that a triangle is isosceles.
|Title||angles of an isosceles triangle|
|Date of creation||2013-03-22 17:12:06|
|Last modified on||2013-03-22 17:12:06|
|Last modified by||Wkbj79 (1863)|