1, because DE=DC, and ∠AED=∠ACD=90, and AD is the public side, so the triangle ACD is congruent with the triangle AED. So ∠CAD=∠EAD

Because AE=BE, ∠AED=∠BED, and DE are common sides, the triangle is congruent with the triangle BED. So ∠B=∠EAD= 1/2∠BAC.

2. Because triangular ACD is equivalent to triangular AED, AC=AE, so AC=BE. Because DE=DC, ∠C=∠BED, ∠CAD=∠EAD=∠B, the triangle ACD is congruent with the triangle BED. Because AC=3, and because the opposite side of 30 degrees is half of the hypotenuse, CD= 1/2AD. Let CD=x, the square of 3+the square of X= the square of (2x), so X = root number 3, so DE= root number 3. Because BE=AE=AC and BE=3, the square of BD = the square of the root number 3+the square of 3, so BD=2 times the root number 3.