Question

If ______, then ∆ABC and ∆EFD are congruent by the ASA criterion.

Answer 1

The correct answers are:

Angle A is congruent to angle E; and BC=FD.

Explanation:

For ASA, we want two angles and an included side of one triangle congruent to two angles and an included side of the other triangle.  The sides we have marked are AC and DE; the angles already marked congruent are C and D.  In order to be ASA, the other angle must be on the other side of the congruent side; this means that we have angles A and E.

For SAS, we want two sides and an included angle of one triangle congruent to two sides and an included angle of the other triangle.  We have angles C and D congruent and sides AC and DE congruent.  In order to be SAS, the other side must be on the other side of the congruent angle; this means we have sides BC and FD.

Answer 2

1.) If angle A is congruent to angle E, then ∆ABC and ∆EFD are congruent by the ASA criterion.
2.) If BC=FD, then ∆ABC and ∆EFD are congruent by the SAS criterion.