Provide the reasons for the proof:
given: trapezoid riag with ri = rg = ga
m angle i = m angle nag
prove: angle t ≈ angle n

Line RG || Line IA = Parallel property of a trapezoid

We know that shape RIAN is a parallelogram with RN || IA and RI || NA
RG is a part of the line RN, so RG is also parallel to IA



m∠TRG = m∠I : Corresponding angle on a transversal

Line TI is a transversal to the parallel lines RN and IA.
m∠TRG and m∠I are corresponding to each other



m∠TGR = m∠NGA: Opposite angles on a transversal

Line TA is a transversal on line RN and IA



ΔTGR = ΔNGA: Opposite angles property in a parallelogram

Opposite angles on a parallelogram are equal



∠T = ∠N: Angle sum of triangle 

∠T = 180° - (∠R + ∠G)
∠N = 180° - (∠G + ∠N)