Question

In the figure below, ∠DEC ≅ ∠DCE, ∠B ≅ ∠F, and segment DF is congruent to segment BD. Point C is the point of intersection between segment AG and segment BD while point E is the point of intersection between segment AG and segment DF.

Answer 1

Answer:

given ∠DEC ≅ DCE, hence DC=CE aslo given DB=Df

hence

DB- DC =DF -CE

BC =EF

given ∠DEC ≅ DCE

but <DCE = <ACB (vert. opposite angles)

but ∠DEC = <GEF (vert. opposite angles)

hence <ACB = <GEF

now in ΔABC and ΔGFE.

BC =EF (proved earlier)

<ACB = <GEF (proved earlier)

∠B ≅ ∠F (given)

hence ΔABC ≅ ΔGFE. (AAS congruency)