Question

what additional piece of information is needed to show that △def ≅ △pqr by asa?
o df ≅ pr
o ∠f ≅ ∠r
o ef ≅ qr
o ∠d ≅ ∠p

Explanation:

Step1: Recall ASA congruence criterion

ASA (Angle - Side - Angle) requires two pairs of corresponding angles and the included side to be congruent.

Step2: Analyze given information

We can see that from the figure, one pair of sides ($DE\cong PQ$) and one pair of angles ($\angle E\cong\angle Q$) are already congruent (indicated by the single - tick mark on the sides and the angle - marking). We need another pair of angles where the congruent side is the included side between the two pairs of angles.

Step3: Determine the needed angle

The angle that, along with the given side and angle, will satisfy ASA is $\angle D\cong\angle P$ since the side $DE$ (in $\triangle DEF$) and $PQ$ (in $\triangle PQR$) is the included side between $\angle D$ and $\angle E$ in $\triangle DEF$ and between $\angle P$ and $\angle Q$ in $\triangle PQR$.

Answer:

$\angle D\cong\angle P$