Triangle BAC was dilated from triangle BDE at a scale factor of 2. What proportion proves that cos∠D = cos∠A?

Triangles BDE and BAC, in which angle B is a right angle, point D is between points B and A, and point E is between points B and C; BD measures 2 units, BE measures 3 units, and DE measures 3 and 61 hundredths units.

2 over 3 and 61 hundredths = 4 over 7 and 22 hundredths
three halves = six fourths
3 over 3 and 61 hundredths = 6 over 7 and 22 hundredths
two thirds = four sixths