Questions: Question 5 of 10 Based only on the information given in the diagram, which congruence theorems or postulates could be given as reasons why triangle DEF is congruent to triangle JKL? Check all that apply. A. AAS B. ASA C. LL D. SAS E. LA F. HL

Solution Steps

We are given two right triangles, ΔDEF and ΔJKL. From the diagram, we know that:

• DE ≅ JK
• EF ≅ KL
• ∠E ≅ ∠K (both are right angles)

We need to determine which congruence theorems can be applied based on the given information.

• AAS (Angle-Angle-Side): We have two congruent angles (the right angles and another pair of congruent angles) and a non-included side (EF and KL). While it appears that the triangles might be congruent by AAS, it is not provable from the provided information alone.
• ASA (Angle-Side-Angle): We have one pair of congruent angles (∠E ≅ ∠K), but no congruent sides adjacent to them are identifiable. Not applicable based on the given information.
• LL (Leg-Leg): We have two pairs of congruent legs (DE ≅ JK and EF ≅ KL). This theorem applies.
• SAS (Side-Angle-Side): We do not have two pairs of congruent sides with the included angle between them. Not applicable with only the given information.
• LA (Leg-Angle): We have a pair of congruent legs (DE ≅ JK) and a pair of congruent angles, which include a right angle. Thus, we have a congruent leg and acute angle, therefore satisfying the LA theorem.
• HL (Hypotenuse-Leg): We have congruent legs (DE ≅ JK and EF ≅ KL), but we haven't definitively identified congruent hypotenuses. However, since the legs are congruent and we have right triangles, LL congruence implies HL congruence. Thus, HL congruence also applies.

Final Answer