Question

select the correct answer. in addition to the facts in the diagram, which statement is necessary to prove that the two triangles are congruent by the sas criterion? a. ac = de b. m∠bac = m∠fde c. bc = ef d. m∠cab = m∠edf

Explanation:

To prove congruence by SAS (Side - Angle - Side), we need two sides and the included angle to be equal. From the diagram, we can see that one pair of sides (the marked sides) and one pair of angles (the marked angles) are likely corresponding. For SAS, we need the other pair of sides that form the included angle with the given side to be equal. In triangle \(ABC\) and \(DEF\), if we consider the angle at \(B\) and \(F\) (the marked angles) and the sides adjacent to these angles, we need \(BC = EF\) to satisfy SAS. Option A gives \(AC = DE\) which is not the side forming the included angle. Option B gives an angle equality which is not the included angle for SAS in this case. Option D gives an angle equality that is not relevant for SAS here. So the correct option is C.

Answer:

C. \(BC = EF\)