Answer:
(d) HA
Explanation:
You have two right triangles with the hypotenuse and one angle marked as congruent. You want to know the applicable theorem for claiming the triangles are congruent.
Right triangle congruence
When two triangles are known to be right triangles, the known angle is opposite the longest side (hypotenuse), and the two legs are the sides that form that known angle. Hence, some special theorems can be invoked for right triangles:
LA — leg, angle; equivalent to ASA
LL — leg, leg; equivalent to SAS
HA — hypotenuse, angle; equivalent to AAS
HL — hypotenuse, leg; no equivalent for non-right triangles
Application
The given triangles have the hypotenuse (H) and an acute angle (A) marked, so the HA theorem can be used to prove congruence.
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Additional comment
The HL condition described above refers two two consecutive sides and the angle not between them (SSA). This set of descriptors will create a unique triangle if and only if the angle is opposite the longest side. In general, that will not be the case, but it is guaranteed to be the case for a right triangle.