9. AM ≅ AT
10. x=3, y=5
AH being the perpendicular bisector of MT means MH ≅ TH. Then ΔAHM ≅ ΔAHT by SAS, and by CPCTC.
... SAS — side-angle-side: if two adjacent sides and the included angle of a triangle are congruent to their corresponding sides and angles in another triangle, the two triangles are congruent.
... CPCTC — Corresponding Parts of Congruent Triangles are Congruent
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Using the result of problem 9 as a guide, you can say that ...
... 2x = x+3 ⇒ . . . . (subtract x from both sides)
... y +4 = 2y -1 ⇒ . . . . (add 1-y to both sides)