To prove the triangles JTB and SDP are congruent by the ASA (Angle-Side-Angle) criteria, we need two angles and the included side to be congruent.
From the information given:
- We have \( \angle TBJ \cong \angle SPD \) (one pair of angles).
- We have \( JB \cong SP \) (the included side between the angles).
To apply ASA, we need another angle to be congruent.
Among the options given:
A. \( \angle T \cong \angle D \) (This would give us another angle, which is needed.) B. \( \angle J \cong \angle S \) (This gives another angle, but it does not help in forming congruence within the requirement of the included side configuration.) C. \( JT \cong SD \) (This would provide a side, but we need another angle, not another side.) D. \( TB \cong DP \) (This also provides a side, which is not what we need.)
Thus, the correct answer is:
A. \( \angle T \cong \angle D \)
This gives the second angle needed to prove the triangles JTB and SDP are congruent by ASA.