Answer
if ∠s ≅ ∠i, ∠g ≅ ∠a, t − midpoint of si, prove sg ≅ ia

angle s ≅ angle i | given
line st ≅ line ti | def. of midpoint
angle g ≅ angle a | given
triangle stg ≅ triangle (put the answer here)
line sg ≅ line ia | corresponding parts of congruent triangles are congruent

Triangle ITA is the answer.

Step-by-step explanation:

<S = <I means that the triangle IRS is an isoscles.

The midpoint (T) cutting both congruent side length sides at the same angle means that Line TG and Line TA are equal.

Also T being the midpoint means Line TI = Line TS.

Given that angles <G and <A are same.

You can use SSA (side-side-angle) to prove triangles are congruent so line SG is equal to Line IA.

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step-by-step explanation: