Question

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Answer 1

see below

Explanation:

ASA congruence theorem: If two angles and the side between two angles of one triangle are congruent to the corresponding angles and side of another triangle, then the two triangles are congruent.

△ABG and △IBG has same side BG, ∠ABG congruent with ∠IBG, ∠AGB congruent with ∠IGB

Therefore △ABG is congruent with △IBG

then IG is congruent with AG

Answer 2

In ΔABG and ΔIBG

∡AGB=∡IGB given

BG=BG reflexive property

∡ABG=∡IBG given

AB=BC given

ΔABG ≅ ΔIBG by ASA (Angle-Side-Angle) axiom.

Since,

The corresponding side of the congruent triangle theorem states that if two triangles are congruent, then all of their corresponding sides are also congruent.

IG=AG being corresponding side of congruent triangle.

Hence Proved.