Answer
Equilateral triangle
Work Step by Step
$\angle$ADE=$\frac{1}{2}$$\angle$D
$\angle$A+$\angle$D=180
$\angle$A+$\angle$ADE+$\angle$AED=180
$\angle$A+$\frac{1}{2}$$\angle$D+$\angle$AED=180
$\angle$A+$\frac{1}{2}$$\angle$D+$\angle$AED=$\angle$A+$\angle$D
$\angle$AED=$\frac{1}{2}$$\angle$D
Since two angles have a measure equal to half of angle D, it must be an equilateral triangle.
