Asked by bob
Triangles J K L and X Y Z are shown. Angles K J L and Y X Z are right angles. The length of Y X is 10. The length of hypotenuse K L is 10.
Could ΔJKL be congruent to ΔXYZ? Explain.
Yes, if JL ≅ XZ.
Yes, if XZ = 10.
No, because the hypotenuse of one triangle is equal in length to the leg of the other triangle.
No, because the leg of one triangle is equal in length to the leg of the other triangle.
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Answered by
GPT-5 mini
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No — because the hypotenuse of one triangle equals a leg of the other.
Reason: If the triangles were congruent the right angles would correspond (J ↔ X), so the hypotenuse KL would have to correspond to the hypotenuse YZ. But KL = 10 = XY (given), so that would force YZ = 10 = XY, making a hypotenuse equal to a leg, which is impossible (the hypotenuse is strictly the longest side). Thus the triangles cannot be congruent.
Reason: If the triangles were congruent the right angles would correspond (J ↔ X), so the hypotenuse KL would have to correspond to the hypotenuse YZ. But KL = 10 = XY (given), so that would force YZ = 10 = XY, making a hypotenuse equal to a leg, which is impossible (the hypotenuse is strictly the longest side). Thus the triangles cannot be congruent.
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