Question

Given: ΔABC, overline AB ≅ overline CB ≅ overline AC

BD - median to AC
EE ≅ overline AB
F in overline BC
AE = CF
Prove: ΔADE ≅ ΔCDF
ΔBDE ≅ ΔBDF

Answer 1

To prove the congruence between ΔADE and ΔCDF, and ΔBDE and ΔBDF, we can use the SAS congruence criterion and the properties of an equilateral triangle.

Step-by-step explanation:

To prove that ΔADE ≅ ΔCDF and ΔBDE ≅ ΔBDF, we can use the SAS (Side-Angle-Side) congruence criterion.

Given that overline AB ≅ overline CB ≅ overline AC, we know that the triangle ABC is an equilateral triangle.

Using the fact that BD is a median to AC, we can conclude that triangle ABD and triangle BCD are congruent by SAS. And since AB = BC, we also have that ΔABE ≅ ΔCBF.