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a) Vì ABCD là hình bình hành nên AB = CD, AB song song CD.

Mà E, F lần lượt là trung điểm của AB, CD nên AE = BE = 1/2 AB, CF = DF = 1/2 CD

Do đó AE = BE = CF = DF.

Xét tứ giác AEFD có:

     AE song song DF (vì AB song song CD);

     AE = DF (chứng minh trên)

Do đó tứ giác AEFD là hình bình hành.

Xét tứ giác AECF có:

     AE song song CF (vì AB song song CD);

     AE song song CF (chứng minh trên)

Do đó tứ giác AECF là hình bình hành.

Vậy hai tứ giác AEFD, AECF là những hình bình hành.

b) Vì tứ giác AEFD là hình bình hành nên EF = AD.

Vì tứ giác AECF là hình bình hành nên AF = EC.

Vậy EF = AD, AF = EC.

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