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Giải bài 9 trang 67 Sách bài tập Toán 6 – Chân trời sáng tạo

Cho lục giác đều ABCDEG a) Hãy đếm các đường chéo của lục giác vẽ từ mỗi đỉnh của lục giác. Hãy cho biết có bao nhiêu đường chéo được đếm 2 lần. b) Hãy cho biết lục giác trên có bao nhiêu đường chéo.

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Cho lục giác đều ABCDEG a) Hãy đếm các đường chéo của lục giác vẽ từ mỗi đỉnh của lục giác. Hãy cho biết có bao nhiêu đường chéo được đếm 2 lần. b) Hãy cho biết lục giác trên có bao nhiêu đường chéo.

Câu a

a) Hãy đếm các đường chéo của lục giác vẽ từ mỗi đỉnh của lục giác. Hãy cho biết có bao nhiêu đường chéo được đếm 2 lần.

Phương pháp giải:

a) Bước 1: Vẽ lục giác và các đường chéo từ đỉnh A. Bước 2: Từ hình vẽ suy ra các đường chéo từ các đỉnh còn lại và đếm số đỉnh được đếm 2 lần.

Lời giải chi tiết:

a) Từ đỉnh A có 3 đường chéo là: AC, AD, AE. Từ đỉnh B có 3 đường chéo là: BD, BE, BG. Từ đỉnh C có 3 đường chéo là: CE, CG, CA. Từ đỉnh D có 3 đường chéo là: DG, DA, DB. Từ đỉnh E có 3 đường chéo là: EA, EB, EC. Từ đỉnh G có 3 đường chéo là: GB, GC, GD. Trong đó 9 đường chéo được đếm 2 lần.

Câu b

b) Hãy cho biết lục giác trên có bao nhiêu đường chéo.

Phương pháp giải:

b) Tính tổng đường chéo. Dựa vào số đường chéo được đếm 2 lần để suy ra số đường chéo của lục giác.

Lời giải chi tiết:

b) Tổng số đường chéo kể cả các đường được đếm 2 lần là: 3 . 6 = 18 (đường) Mà mỗi đường chéo đều đước đếm 2 lần, do đó số đường chéo của lục giác là: 18 : 2 = 9 (đường chéo)

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