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Giải câu hỏi trắc nghiệm trang 75, 76 vở thực hành Toán 8

Chọn phương án đúng trong mỗi câu sau:

🉐Tổng hợp đề thi học kì 2 lớp 8 tất cả các môn - Kết nối tri thức

Toán - Văn - Anh - Khoa học tự nhiên
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Lựa chọn câu để xem lời giải nhanh hơn
Chọn phương án đúng trong mỗi câu sau:

Câu 1 trang 75

Quan sát Hình 4.17 và chọn khẳng định đúng.

 

A. \(\frac{{IA}}{{IC}} = \frac{{BA}}{{AC}}.\) B. \(\frac{{IA}}{{IC}} = \frac{{BC}}{{BA}}.\) C. \(\frac{{IA}}{{IC}} = \frac{{BA}}{{BC}}.\) D. \(\frac{{IA}}{{IC}} = \frac{{AC}}{{AB}}.\)

Phương pháp giải:

Dựa vào tính chất đường phân giác của tam giác: Trong tam giác, đường phân giác của một góc chia cạnh đối diện thành hai đoạn thẳng tỉ lệ với hai cạnh kề hai đoạn thẳng ấy.

Lời giải chi tiết:

Ta có IB là đường phân giác của góc B nên \(\frac{{IA}}{{IC}} = \frac{{AB}}{{BC}}.\) => Chọn đáp án C.

Câu 2 trang 75

Quan sát Hình 4.18, biết BI là phân giác của góc B, AB = 12 cm, BC = 15 cm, AC = 9 cm. Độ dài đoạn IA là:

 

A. 5 cm. B. 4 cm. C. 6 cm. D. 3 cm.

Phương pháp giải:

Dựa vào tính chất đường phân giác của tam giác: Trong tam giác, đường phân giác của một góc chia cạnh đối diện thành hai đoạn thẳng tỉ lệ với hai cạnh kề hai đoạn thẳng ấy.

Lời giải chi tiết:

Ta có BI là phân giác của góc B nên \(\frac{{IA}}{{AB}} = \frac{{IC}}{{BC}} = \frac{{IA + IC}}{{AB + BC}} = \frac{{AC}}{{AB + BC}} = \frac{9}{{12 + 15}} = \frac{9}{{27}} = \frac{1}{3}\) Do đó \(IA = \frac{1}{3} \cdot AB = \frac{1}{3} \cdot 12 = 4\) (cm).  => Chọn đáp án B.

Câu 3 trang 76

Quan sát Hình 4.19. Tỉ số \(\frac{x}{y}\) bằng

 

A. \(\frac{1}{7}\). B. \(\frac{{15}}{7}\) C. \(\frac{7}{{15}}\) D. \(\frac{2}{{15}}\)

Phương pháp giải:

Dựa vào tính chất đường phân giác của tam giác: Trong tam giác, đường phân giác của một góc chia cạnh đối diện thành hai đoạn thẳng tỉ lệ với hai cạnh kề hai đoạn thẳng ấy.

Lời giải chi tiết:

Ta có AD là phân giác của góc A nên \(\frac{{DB}}{{DC}} = \frac{{AB}}{{AC}}\). Do đó \(\frac{x}{y} = \frac{{3,5}}{{7,5}} = \frac{7}{{15}}.\) => Chọn đáp án C.

Câu 4 trang 76

Quan sát Hình 4.20. Độ dài x, y lần lượt là:

 

A. x = 16 cm; y = 12 cm. B. x = 14 cm; y = 14 cm. C. x = 14,3 cm; y = 10,7 cm. D. x = 12 cm; y = 16 cm.

Phương pháp giải:

Dựa vào tính chất đường phân giác của tam giác: Trong tam giác, đường phân giác của một góc chia cạnh đối diện thành hai đoạn thẳng tỉ lệ với hai cạnh kề hai đoạn thẳng ấy.

Lời giải chi tiết:

Ta có AD là phân giác của góc A nên \(\frac{{DB}}{{DC}} = \frac{{AB}}{{AC}}\). Khi đó \(\frac{x}{{15}} = \frac{y}{{20}} = \frac{{x + y}}{{15 + 20}} = \frac{{28}}{{35}} = \frac{4}{5}\). Do đó \(x = \frac{4}{5} \cdot 15 = 12\,\,\left( {cm} \right);y = \frac{4}{5} \cdot 20 = 16\,\,\left( {cm} \right).\) => Chọn đáp án D.

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