Answer:
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}
[tex]\overline {AC} \cong \overline{GE}\ \textrm{......Proved}[/tex]
