Why is the resistance of DC equal to resistance of AC?

Resistance to AC is only the same as DC in a purely resistive circuit. Something like a heating element.

When we apply AC other types of loads like a motor there is a reactance that appears as a resistance to AC and not DC. This is due to the coils of windings inside the motor having inductance. We call this inductive reactance. Inductive reactance opposes a change in current and since AC current is always changing so the reactance is always seen by an AC current and not a DC current. This reaction cause the current to lag behind the voltage. The symbol for inductive reactance is Xl. L being the symbol for inductance.

As similar reactance occurs to AC when applied to capacitive loads but in a different way to inductive reactance.

A capacitive load causes the voltage to lag behind the current when AC is applied to a capacitor. We call this reactance Xc.

Capacitive reactance and inductive reactance tend to cancel each other out depending on the values of inductance, and capacitance. The frequency of the AC affects each in an opposite manners too.

When the resistance , inductive reactance (Xl), and capacitive reactance Xc are combined (by vectors) they form a term called Impedance symbol “Z”. Impedance “Z” is the total “resistance” to AC. A pure resistance does not react to AC at low frequencies like 50 or 60 Hz as much as with the other types of loads and generally ignored because it is so small.

So your statement is only true for purely resistive loads and most loads connected to AC are a combination of resistance, inductance and capacitance.