1.证明:(1)因为AB=AC,A′B′=A′B′,所以AB/A'B'=AC/A'C',且∠A=∠A′,所以△ABC∽△A′B′C′.
(2)因为AB=AC,所以∠B=∠C,因为A′B′=A′C′,所以∠B′=∠C′,因为∠B=∠B′,所以∠C=∠C′,所以△ABC∽△A′B′C′.
2.解:△ABC∽△A_2 B_2 C_2.理由如下:因为△ABC∽△A_1 B_1 C_1,所以∠A=∠A_1,∠B=∠B_1,又因为△A_1 B_1 C_1∽△A_2 B_2 C_2,所以∠A_1=∠A_2,∠B_1=B_2=∠B_2,所以∠A=∠A_2,∠B=∠B_2,所以△ABC∽△A_2 B_2 C_2.
3.解:△OCD∽△OAB,OC/OA=OD/OB=CD/AB.