Question

fill in the missing statement and reason of the proof below.given: $angle ahb cong angle eid$, $bg cong dg$ and $bc cong dc$.prove: $\triangle bgf cong \triangle dgf$.step | statement | reason1 | $angle ahb cong angle eid$ <br> $bg cong dg$ <br> $bc cong dc$ | given2 | $gc cong gc$ | reflexive property3 | $\triangle bgc cong \triangle dgc$ | sss4 | $angle bgf cong angle dgf$ | corresponding parts of congruent triangles are congruent (cpctc)5 | $angle gfh cong angle ahb$ | vertical angles are congruent6 | missing statement |7 | $angle gfh cong angle dif$ | transitive property8 | $gf cong gf$ | reflexive property9 | $\triangle bgf cong \triangle dgf$ | asa

Explanation:

Step1: Identify congruent angles

From steps 4 and 5, we know $\angle BGF \cong \angle DGF$ and $\angle GHF \cong \angle AHB$. Also given $\angle AHB \cong \angle EID$.

Step2: Apply transitive property

Since $\angle GHF \cong \angle AHB$ and $\angle AHB \cong \angle EID$, by transitive property of congruence:
$\angle GHF \cong \angle EID$

Answer:

$\boldsymbol{\angle GHF \cong \angle EID}$