Kirchhoff’s Law and Superposition Theorem
simulate this circuit &ndash; Schematic created using CircuitLab

First of all, mark all currents on all branches with their magnitude and direction as you calculated.

To verify Kirchoff's current law:


For node E, consider currents entering and leaving the node - \$I_{R1}, I_{R2}, I_{R3} \$
Similarly for node G, consider currents - \$I_{R3}, I_{DG}, I_{GB} \$
Prove that the algebraic sum of currents leaving the node = algebraic sum of currents entering the node. 


To verify Kirchoff's voltage law:


Consider all 3 loops in the circuit - AEGB, ECDG, ACDB.
Prove that the sum of all voltage drops and voltage sources = 0 in each loop.