Question

step statement reason
1 abcd is a rhombus given
∠bae ≅ ∠bcf
2 ∠dab ≅ ∠dcb opposite angles of a parallelogram / rhombus / rectangle / square are congruent
3 ∠ead ≅ ∠fcd select a reason...

Explanation:

Step 1: Analyze the given angles

We know that \( \angle DAB\cong\angle DCB\) (opposite angles of a rhombus are congruent) and \( \angle BAE\cong\angle BCF\) (given).

Step 2: Use the angle - subtraction property

If \( \angle DAB=\angle BAE+\angle EAD\) and \( \angle DCB=\angle BCF + \angle FCD\), and since \( \angle DAB\cong\angle DCB\) and \( \angle BAE\cong\angle BCF\), then by the subtraction property of congruent angles (\( \text{If }a = b + c\), \(a'=b'+c'\), \(a\cong a'\), \(b\cong b'\), then \(c\cong c'\)), we can say that \( \angle EAD\cong\angle FCD\).

Answer:

Subtraction property of congruent angles.