14.
∠A ≅ ∠T . . . . given
AX ≅ TX . . . . given
∠AXM ≅ ∠TXH . . . . vertical angles are congruent
ΔAXM ≅ ΔTXH . . . . ASA theorem
MX ≅ HX . . . . CPCTC
___
15.
The acronyms that invoke theorems based on two or three sides being congruent are inapplicable in this case.
SSS
SAS