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Answer:
1. HA is equivalent to AAS when the triangle is a right triangle.
2. AM = BM, so the triangles are congruent by HL. CPCTC
3. The triangles are congruent by HL. CPCTC
Step-by-step explanation:
1. The acute angle of the triangle together with the right angle comprise two angles of the triangle. When two corresponding angles and a corresponding side (the side opposite the right angle) are congruent, the right triangles are congruent by the AAS theorem. (This can be referred to as the HA theorem.)
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2. CM = DM; MA = MB; ∠A = ∠C = 90°, so all of the requirements for the HL theorem are met. ΔCMA ≅ ΔDMB, so AC ≅ BD by CPCTC.
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3. TS = TV, TR = TR, ∠S = ∠V = 90°, so all requirements for the HL theorem are met. ΔTSR ≅ ΔTVR, so RS ≅ RV by CPCTC.