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Bài 4.16 trang 105 SGK Toán 11 tập 1 - Cùng khám phá

Trong giờ học bóng đá, khi hai bạn Nam và Mai lại gần khung thành thủ môn, bạn Nam khẳng định thanh ngang trên cùng của khung thành và bóng của nó là hình ảnh của hai đường thẳng song song.
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Đề bài

Trong giờ học bóng đá, khi hai bạn Nam và Mai lại gần khung thành thủ môn, bạn Nam khẳng định thanh ngang trên cùng của khung thành và bóng của nó là hình ảnh của hai đường thẳng song song. Bạn Mai cho rằng hai đường thẳng này chưa chắc song song vì còn phụ thuộc vào ảnh hưởng của ánh sáng Mặt Trời nữa. Hãy cho biết ai đúng, ai sai. Vì sao? Biết rằng, Mặt Trời cách xa Trái Đất nên các tia sáng có thể xem là những đường thẳng song song.

Phương pháp giải - Xem chi tiết

Áp dụng định lý: Cho đường thẳng a song song với mặt phẳng (P). Nếu mặt phẳng (Q) chứa a và cắt (P) theo giao tuyến b thì b song song với a.

Lời giải chi tiết

Gọi thanh ngang trên cùng của khung thành là a, mặt đất là (P). Các tia sáng song song tạo thành mặt phẳng (Q). Khi đó bóng của thanh ngang chính là giao tuyến của (P) và (Q). Gọi giao tuyến này là b.Suy ra a và b phải luôn song song với nhau.Vậy bạn Nam nói đúng, Mai nói sai.

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