Question

Determine the correctness of the proofsThe proof below may or may not be correct. If the proof is incorrect, determine the first step number that is not justified and the reason it is not justified.

Answer 1

Analyzing each statement and reason, we have:

1.

All these statements are given, so this step is ok.

2.

The sides AD and DC are corresponding sides between triangles DEA and DFC, so this step is ok.

3.

Here the transitive property is used to switch AD by AB, which is a given statement (AD = AB), so this step is ok.

4.

Since angles DAB and FDC are congruent and are corresponding angles in a transversal, the sides AB and DC are parallel, the reason is correct, so this step is ok.

5.

If we have one pair of opposite, parallel and congruent sides in a quadrilateral, this quadrilateral is a parallelogram. The reason is correct, and this step is ok.

Since all steps are correct, the proof is correct.