What additional information will allow you to prove the triangles congruent by the HL Theorem?
m< TWR = 90 degrees
TW¯¯¯¯¯¯¯¯¯≅PR¯¯¯¯¯¯¯¯
∠P≅∠R
TW¯¯¯¯¯¯¯¯¯≅WS¯¯¯¯¯¯¯¯¯
To prove the triangles congruent by the HL theorem, we would need the following additional information:
1) One of the angles in triangle PRW must be congruent to one of the angles in triangle SWR (in addition to the given congruent angles ∠P ≅ ∠R).
2) One of the sides in triangle PRW must be congruent to one of the sides in triangle SWR (in addition to the given congruent sides TW ¯¯¯¯ ≅ WS ¯¯¯¯).
This information is necessary because the HL (Hypotenuse-Leg) theorem states that if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the triangles are congruent. Therefore, we need congruent angles and congruent sides (in addition to the right angle) in order to apply the HL theorem and prove the triangles congruent.