Infographic Geometry Problem 1173: Triangle, Cevian, Angle, Congruence, Similarity. Level: High School, College, Mathematics Education

In a triangle ABC (see the figure), D is on BC and E on AC such that AB = 6, BD = 4, DC = 5, and AD = AE.
Prove that (1) angle BAD = angle C; (2) angle ABD = 2 angle CDE, (3) AD = 2CE.
ELEMENTARY GEOMETRY ONLY PLS
This entry contributed by Sumith Peiris.