Find two consecutive integers whose sum is the square of 7

Step-by-step explanation:

Two consecutive integers be x  and (x+1)

x + x +1 = 7²

2x + 1 = 49

2x = 49 - 1

2x = 48

x = 48/2

x = 24

The consecutive integers are: 24,25

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.