cho tam giác ABC vẽ B' và C' lần lượt đối xứng với B và C qua A. Chứng minh rằng:
a) B'C'=BC
b)B'C'//BC
Ai nhanh mik tik nha
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tham khảo:
a) Tam giác AOB có A'B' là đường trung bình nên A'B'//AB hay A'B'//(OBC)
Tam giác AOC có A'C' là đường trung bình nên A'C"//AC hay A'C'//(OBC)
Suy ra (A'B'C')//(OBC)
Mà OA⊥(OBC) nên OA⊥(A′B′C′)
b) Vì OA⊥(OBC);BC∈(OBC) nên OA⊥CB
Ta có đường thẳng BC vuông góc với hai đường thẳng OH và OA cắt nhau cùng thuộc (AOH) nên BC⊥(OAH)
Mà tam giác ABC có B'C' là đường trung bình nên B'C'//BC
Suy ra B′C′⊥(AOH)
Cho tam giác ABC cân (AB = AC). Gọi C’ là điểm đối xứng của Cqua AB, gọi B’ là điểm đối xứng của B qua AC. Vẽ phân giác AD.
1) C/m: B’C’ vuông góc với AD
2) C/m: DB’ = DC’