Giáo dụcLớp 7

Toán 7 Bài 1: Góc và cạnh của một tam giác

 

Giải bài tập SGK Toán 7 Tập 2 trang 44, 45, 46, 47 sách Chân trời sáng tạo giúp các em học sinh lớp 7 xem gợi ý giải các bài tập của Bài 1: Góc và cạnh của một tam giác.

Thông qua đó, các em sẽ biết cách giải toàn bộ các bài tập của bài 1 Chương 8 – Tam giác trong sách giáo khoa Toán 7 Tập 2 Chân trời sáng tạo. Đồng thời, cũng giúp thầy cô tham khảo để soạn giáo án cho học sinh của mình theo chương trình mới. Vậy mời thầy cô và các em cùng theo dõi bài viết dưới đây của Download.vn:

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Giải Toán 7 Chân trời sáng tạo trang 46, 47 tập 2

Bài 1

Tìm số đo các góc chưa biết của các tam giác trong Hình 5.

Hình 5

Gợi ý đáp án:

a. \widehat{A} =180^{o}-\widehat{A}-\widehat{C}= 180^{0} - 72^{0} - 44^{0} = 64^{0}

b. \widehat{D} =180^{o}-\widehat{E}-\widehat{F}= 180^{0} - 59^{0} - 31^{0} = 90^{0}

c. \widehat{M} = 180^{o}-\widehat{N}-\widehat{P}= 180^{0} - 120^{0} - 33^{0} = 27^{0}

Bài 2

Tìm số đo của góc x trong Hình 6

Hình 6

Gợi ý đáp án:

a) Gọi H là chân vuông góc kẻ từ M xuống cạnh NL.

Xét tam giác NML vuông tại M có: \widehat{L} = 180^{0} - 90^{0} - 62^{0} = 28^{0}.

Xét tam giác MLH vuông tại H có: \widehat{M} + \widehat{L} = 180^{o}-90^{0}=62^{0}.

Vậyx = 62^{0}.

b) Gọi K là chân đường vuông góc kẻ từ Q xuống cạnh RP.

Xét tam giác QRK có \widehat{QHR} = 90^{0}

Nên \widehat{RQK} = 90^{0} - \widehat{R} = 90^{0} - 52^{0} = 38^{0}

\widehat{RQP} = 90^{0}= \widehat{RQK}+\widehat{KQP}

\Rightarrow x = 90^{0} - \widehat{RQK} = 90^{0} - 38^{0} = 52^{0}.

Vậy x = 52^{0}.

Bài 3

Hãy chia tứ giác ABCD trong hình 7 thành hai tam giác để tính tổng số đo của bốn góc \widehat{A} , \widehat{B}, \widehat{C}, \widehat{D}.

Hình 7

Gợi ý đáp án:

Hình 7

Nối đoạn thẳng BD.

Xét tam giác ABD có: \widehat{A}+\widehat{ABD}+\widehat{ADB}=180^{o}.

Xét tam giác BDC có: \widehat{C}+\widehat{CBD}+\widehat{CDB}=180^{o}.

\Rightarrow \widehat{A} + \widehat{B}+\widehat{C}+\widehat{D} = \widehat{A}+\widehat{ABD}+\widehat{CBD}+\widehat{ADB} + \widehat{CDB} +\widehat{C}

= 180^{o} + 180^{o} = 360^{o}

Vậy \widehat{A} + \widehat{B}+\widehat{C}+\widehat{D} = 360^{o}

Bài 4

Trong các bộ ba độ dài đoạn thẳng dưới đây, bộ ba nào có thể là độ dài ba cạnh của một tam giác?

a) 4cm, 5cm, 7cm

b) 2cm, 4cm, 6cm

c) 3cm, 4cm, 8cm

Gợi ý đáp án:

a) 5 – 4 < 7 < 4 + 5.

b) 2+ 4 = 6.

c) 3 + 4 < 8.

Trong các bộ ba độ dài đoạn thẳng dưới đây, bộ ba câu a) 4cm, 5cm, 7cm có thể là độ dài ba cạnh của một tam giác.

Bài 5

Cho tam giác ABC có BC = 1cm, AB = 4cm. Tìm độ dài cạnh AC (theo đơn vị cm), biết rằng độ dài này là một số nguyên.

Gợi ý đáp án:

Áp dụng đính lí về độ dài 3 cạnh của một tam giác ta có: 4 – 1 < AC < 4 + 1, hay 3 < AC < 5.

Vì độ đài AC là một số nguyên, nên độ dài AC có thể là: 4.

Thử lại giá trị vừa tìm được 5 < 3 + 4 thỏa mãn định lí.

Vậy độ dài AC = 4cm.

Bài 6

Trong một trường học, người ta đánh dấu ba khu vực A, B, C là ba đỉnh của một tam giác, biết khoảng cách AC = 15m, AB = 45m.

a. Nếu đặt ở khu vực C một thiết bị phát wifi có bán kính hoạt động 30m thì tại khu vực B có nhận được tín hiệu không? Vì sao?

b. Cũng câu hỏi như trên với thiết bị phát wifi có bán kính hoạt động 60m.

Gợi ý đáp án:

Áp dụng định lí về độ dài 3 cạnh của một tam giác có: 45 – 15 < BC < 45 + 15, hay 30 < BC < 60.

a) Nếu đặt ở khu vực C một thiết bị phát wifi có bán kính hoạt động 30 m thì khu vực B không nhận được tín hiệu vì BC > 30 m.

b) Nếu đặt ở C một thiết bị phát wifi có bán kính hoạt động 60 m thì khu vực B nhận được tín hiệu vì BC < 60 m.

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Chuyên mục: Giáo dục, Lớp 7

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