Every Friday the boss buys pizza for his workers. Last week the workers finished 5 pizzas. This week they finished 5 pizzas. Write the ratio of pizzas eaten last week to pizzas eaten this week.
Remember ratios must have two whole numbers.

1:1 because they ate the same amount both weeks

AC bisects ∠BAD, => ∠BAC=∠CAD (1)

thus in ΔABC and ΔADC,    ∠ABC=∠ADC (given),

                                      ∠BAC=∠CAD      [from (1)],

AC (opposite side side of ∠ABC) = AC (opposite side side of ∠ADC), the common side between ΔABC and ΔADC

Hence,      by AAS axiom, ΔABC ≅ ΔADC,

Therefore,  BC (opposite side side of ∠BAC) = DC (opposite side side of ∠CAD),  since (1)

Hence, BC=DC proved.