∵△ABC∽△A1B1C1,∴∠A=∠A1,∠B=∠B1,∴∠C=∠C1,
又∵△A1B1C1∽△A2B2C2,∴∠A2=∠A1,∠B2=∠B1,∴∠C2=∠C1,
∴∠A=∠A2,∠B=∠B2,∴∠C=∠C2,
∴△ABC∽△A2B2C2