Question

complete the proof that \overleftrightarrow{ab} \parallel \overleftrightarrow{cg}.
step | statement | reason
1 | cf = ae | both circles have radii of the same length.
2 | cg = ad | both circles have radii of the same length.
3 | \square | both circles have radii of the same length.
4 | \triangle ade \cong \triangle cgf | side - side - side congruence (1, 2, 3)
5 | \square | corresponding parts of congruent triangles are congruent

Explanation:

Step 3: Identify the third side

To prove the triangles congruent by SSS, we need a third pair of equal sides. From the diagram and the context (circles with same radii), the third side should be \( DE = GF \) (since both would be radii of the same - sized circles or constructed similarly). So the statement for step 3 is \( DE = GF \).

Step 5: Corresponding angles

Since \( \triangle ADE\cong\triangle CGF \) by SSS, the corresponding angles \( \angle ADE\cong\angle CGF \). These are corresponding angles formed by the transversal \( AD \) (or \( CG \)) with the lines \( AB \) and \( CG \). If corresponding angles are congruent, then the lines are parallel. So the statement for step 5 is \( \angle ADE\cong\angle CGF \) (which leads to \( \overleftrightarrow{AB}\parallel\overleftrightarrow{CG} \) by corresponding angles postulate).

Answer:

Step 3: \( DE = GF \)
Step 5: \( \angle ADE\cong\angle CGF \)