Question

∠fba≅∠fdc alternate interior angles theorem
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\\(\frac{fb}{fd}=\frac{af}{cf}\\) corresponding sides in similar triangles are proportional.
\\(\frac{fb}{af}=\frac{fd}{cf}\\) division property of equality
slope of \\(\overline{ab}=\frac{fb}{af}\\) definition of slope
slope of \\(\overline{dc}=\frac{fd}{cf}\\)
slope of \\(\overline{ab}=\\) slope of \\(\overline{dc}\\) substitution property of equality
which step is missing?
a. statement: △fdc∼△fab reason: aa
b. statement: △fdc∼△fba reason: aa
c. statement: △fdc≅△fba reason: sas
d. statement: △fdc≅△fab reason: sas

Explanation:

Step1: Analyze the given information

We know that $\angle FBA\cong\angle FDC$ (by alternate - interior angles theorem). Also, $\angle BFA\cong\angle DFC$ (vertically - opposite angles are equal).

Step2: Recall similarity criteria

The AA (angle - angle) similarity criterion states that if two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar.

Step3: Determine the missing step

Since we have two pairs of congruent angles ($\angle FBA\cong\angle FDC$ and $\angle BFA\cong\angle DFC$), the two triangles $\triangle FDC$ and $\triangle FAB$ are similar by the AA similarity criterion.

Answer:

A. Statement: $\triangle FDC\sim\triangle FAB$ Reason: AA