hat information would be sufficient to prove that the triangles are congruent by the HL Theorem? Choose the correct answer below. A. LJ=30 and GK=30 B. GK=30 C. GL=9 D. GL=9 and HK=15

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 two triangles are congruent.From the picture details, we know that:- Triangle GJH and triangle LKH are right triangles (since ∠G and ∠K are right angles).- GH = 15, which is the length of one leg of triangle GJH.- HJ = 9, which is the length of the other leg of triangle GJH.- ∠GHJ = ∠LHK, which means the triangles have one pair of congruent angles.To use the HL Theorem, we need to prove that the hypotenuse and one leg of triangle LKH are congruent to the hypotenuse and one leg of triangle GJH.Let's evaluate the options:A. LJ = 30 and GK = 30This option does not help because LJ is not a side of either right triangle, and while GK = 30 would give us the length of one leg of triangle LKH, we still don't have the length of the hypotenuse of triangle LKH to compare with GH.B. GK = 30This option gives us the length of one leg of triangle LKH, but without the length of the hypotenuse of triangle LKH, we cannot use the HL Theorem.C. GL = 9This option does not help because GL is not a side of either right triangle.D. GL = 9 and HK = 15This option gives us the length of the hypotenuse of triangle LKH (HK = 15) and one leg of triangle GJH (HJ = 9). However, GL = 9 is not relevant because GL is not a side of either right triangle.The correct information needed to prove that the triangles are congruent by the HL Theorem would be the length of the hypotenuse and one leg of triangle LKH. Since GH = 15 is the hypotenuse of triangle GJH and HJ = 9 is a leg of triangle GJH, we need the corresponding sides of triangle LKH to be congruent to these.Therefore, the correct answer is not listed in the options provided. To prove the triangles congruent by the HL Theorem, we would need to know that HK (the hypotenuse of triangle LKH) is equal to GH (the hypotenuse of triangle GJH), which is 15, and that LK (the leg of triangle LKH) is equal to HJ (the leg of triangle GJH), which is 9. Since none of the options provide this information, none of the answers A, B, C, or D are correct.