Cho tam giác ABC. Phía ngoài tam giác ABC dựng hình vuông BCGF, ACHI. Gọi O, A', B' lần lượt là trung điểm của AB, BG, AH.Chứng minh rằng :
a) AG=BH
b) AG vuông góc BH
c) Tam giác OA'B' vuông cân
K
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CM
14 tháng 2 2018
a) Phép quay tâm C góc 90 ο biến MB thành AI. Do đó MB bằng và vuông góc với AI. DP song song và bằng nửa BM, DO song song và bằng nửa AI. Từ đó suy ra DP bằng và vuông góc với DO.
b) Từ câu a) suy ra phép quay tâm D, góc 90 ο biến O thành P, biến A thành Q. Do đó OA bằng và vuông góc với PQ.
16 tháng 9 2019
tự kẻ hình :
có M; N lần lượt là trung điểm của AB; AC (gt)
=> MN là đường tb của tam giác ABC (đn)
=> MN // BC (đl)
góc BCNM là tứ giác
=> BCNM là hình thang (đn)
