3a)
1. ∠T ≅ ∠T . . . . reflexive property of congruence
2. ∠TAN ≅ ∠TRI . . . . corresponding angles postulate
3. ΔTAN ~ ΔTRI . . . . AA similarity theorem
3b)
Corresponding parts of similar triangles are proportional, so ...
... NI/AR = TN/AT
... NI/(2 cm) = (12 cm)/(8 cm)
... NI = (2 cm)·(12/8)
... NI = 3 cm