Question

Provide the reasons for the proof:

Given: Trapezoid RIAG with RI = RG = GA
m angle I = m angle NAG
Prove: angle T ≈ angle N

Answer 1

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

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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

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

Line TA is a transversal on line RN and IA

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ΔTGR = ΔNGA: Opposite angles property in a parallelogram

Opposite angles on a parallelogram are equal

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∠T = ∠N: Angle sum of triangle

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