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Answer :
The Hypotenuse-Angle (HA) Theorem states that if two right triangles have the same hypotenuse and one acute angle, then the triangles are congruent. The correct option ic D. HA.
The Hypotenuse-Angle (HA) Theorem states that if two right triangles have the same hypotenuse and one acute angle, then the triangles are congruent. This is because the other acute angle must also be the same, and the corresponding sides of congruent triangles must be equal in length.
In the image you provided, we have two right triangles, △HIJ and △KLM, where HJ and KL are the hypotenuses and ∠JIH and ∠LKM are acute angles. We are given that HJ=KL and JIH=LKM. Therefore, by the HA Theorem, △HIJ≅△KLM.
We can also see this is true by looking at the image. The two triangles are identical in shape and size, so they must be congruent.
Therefore, the answer is D. AA.
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