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Giải bài tập 9.44 trang 92 SGK Toán 9 tập 2 - Kết nối tri thức

Bạn Lan muốn cắt hình ngôi sao có dạng như Hình 9.62 (trong đó ABCDE là một ngũ giác đều). Lan gấp đôi tờ giấy, vẽ một nửa ngôi sao và cắt theo nét vẽ. Góc tạo bởi lưỡi kéo và nếp gấp lúc đầu bằng bao nhiêu?

Tổng hợp Đề thi vào 10 có đáp án và lời giải

Toán - Văn - Anh
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Đề bài

Bạn Lan muốn cắt hình ngôi sao có dạng như Hình 9.62 (trong đó ABCDE là một ngũ giác đều). Lan gấp đôi tờ giấy, vẽ một nửa ngôi sao và cắt theo nét vẽ. Góc tạo bởi lưỡi kéo và nếp gấp lúc đầu bằng bao nhiêu?

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

+ Tính được góc trong ngũ giác đều bằng \({108^o}\). + Tính được \(\widehat {HAB} = \widehat {HBA} = {180^o} - {108^o} = {72^o}\) nên \(\widehat {AHB} = {180^o} - \widehat {HAB} - \widehat {HBA} = {180^o} - {72^o} - {72^o} = {36^o}\) + Góc tạo bởi lưỡi kéo và nếp gấp lúc đầu bằng \(\frac{1}{2}\widehat {AHB} = \frac{1}{2}{.36^o} = {18^o}\).

Lời giải chi tiết

Xét ngũ giác đều ABCDE, ta thấy tổng 5 góc của ngũ giác đều đó bằng tổng các góc trong ba tam giác ABC, ACD, ADE, tức là bằng \({3.180^o} = {540^o}\). Do tất cả các góc của ngũ giác đều bằng nhau nên số đo mỗi góc của ngũ giác đều bằng \(\frac{{{{540}^o}}}{5} = {108^o}\). Do đó, \(\widehat {EAB} = \widehat {ABC} = {108^o}\). Suy ra: \(\widehat {HAB} = \widehat {HBA} = {180^o} - {108^o} = {72^o}\). Tam giác HAB có: \(\widehat {AHB} = {180^o} - \widehat {HAB} - \widehat {HBA} = {180^o} - {72^o} - {72^o} = {36^o}\) Do đó, góc tạo bởi lưỡi kéo và nếp gấp lúc đầu là: \(\frac{1}{2}\widehat {AHB} = \frac{1}{2}{.36^o} = {18^o}\).

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Tham Gia Group Dành Cho Lớp 9 - Ôn Thi Vào Lớp 10 Miễn Phí

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