How does this get solved? i am a bit confused on what to do next. is very appreciated.

The Proof is given below.

Step-by-step explanation:

Given:

AD ≅ BD ≅ FD ≅ GD

To Prove:

AC ≅ GE

Proof:

In  Δ ADF and Δ  GDB

AD ≅ DG     ……….{Given}

∠ ADF ≅ ∠ BDG    …………..{Vertically Opposite angles are equal}

FD ≅ BD     ……….{Given}

Δ ADF ≅ Δ GDB ….{Side-Angle-Side test}

∴∠ FAD ≅  ∠ BGD .....{corresponding angles of Congruent Triangle ( c.p.c.t}

i.e ∠ CAD ≅  ∠ EGD.....{ F-C-A  and B-E-G straight line}.......( 1 )

Now ,

In  Δ CAD and Δ E GD

∠ CAD ≅  ∠ EGD    ……….{From ( 1 ) above}

AD ≅ GD     ……….{Given}

∠ ADC ≅ ∠ EDG    …………..{Vertically Opposite angles are equal}

Δ ADF ≅ Δ GDB ….{Angle-Side-Angle test}

∴ AC ≅   GE .....{corresponding sides of Congruent Triangle ( c.p.c.t}

ljn

step-by-step explanation: