Giải bài 67 trang 85 sách bài tập toán 8 – Cánh diều

Một chiếc kệ bày hoa quả có ba tầng được thiết kế như Hình 59. Tầng đáy có đường kính $AB$ là 32 cm.

🍌Tổng hợp đề thi học kì 2 lớp 8 tất cả các môn - Cánh diều

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Đề bài

Một chiếc kệ bày hoa quả có ba tầng được thiết kế như Hình 59. Tầng đáy có đường kính $AB$ là 32 cm. Tầng giữa có đường kính $CD$ nhỏ hơn đường kính tầng đáy là 12 cm. Tính độ dài đường kính tầng trên cùng $EF$, biết $EF//AB$; $D,C$ lần lượt là trung điểm của $EA$ và $FB$.

Phương pháp giải - Xem chi tiết

Tam giác $A'B'C'$ gọi là đồng dạng với tam giác $ABC$ nếu: $\widehat{A'}=\widehat{A},\widehat{B'}=\widehat{B},\widehat{C'}=\widehat{C}$ ; $\frac{A'B'}{AB}=\frac{B'C'}{BC}=\frac{A'C'}{AC}$. Kí hiệu là $\Delta A'B'C'\backsim \Delta ABC$. Tỉ số các cạnh tương ứng $\frac{A'B'}{AB}=\frac{B'C'}{BC}=\frac{C'A'}{CA}=k$ gọi là tỉ số đồng dạng.

Lời giải chi tiết

Tầng giữa có đường kính $CD$ là: $32-12=20$cm.Ta có: $EF//AB;D,C$ lần lượt là trung điểm của $EA$ và $FB$$=>DC//EF//AB$Xét hai tam giác $EHD$ và $EAB$ có $DH//AB=>\Delta EHD\backsim \Delta EAB$$ =>\frac{DE}{AE}=\frac{DH}{AB}=\frac{1}{2} \\ =>DH=\frac{AB.DE}{AE}=\frac{32.1}{2}=16cm $Độ dài $HC=DC-DH=20-16=4$cm.Xét hai tam giác $BHC$ và $BEF$ có $HC//EF=>\Delta BHC\backsim \Delta BEF$$ =>\frac{HC}{EF}=\frac{BC}{BF}=\frac{1}{2} \\=>EF=2.HC=2.4=8cm \\$Vậy độ dài đường kính tầng trên cùng $EF=8$cm.

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💜 Giải bài 68 trang 85 sách bài tập toán 8 – Cánh diều Cho tam giác $ABC$ có ba góc nhọn, điểm $I$ thuộc cạnh $BC$ và $IM,IN$ lần lượt là đường phân giác của các góc $AIC$ và $AIB$. Chứng minh: $AN.BI.CM=BN.IC.AM$.
🅘 Giải bài 69 trang 85 sách bài tập toán 8 – Cánh diều Cho tam giác $ABC$ cân tại $A,AB=10$cm, $BC=12$cm. Gọi $I$ là giao điểm của các đường phân giác của tam giác $ABC$. Tính độ dài $AI$.
🉐 Giải bài 70 trang 85 sách bài tập toán 8 – Cánh diều Cho tam giác $ABC$ có ba góc nhọn, các đường cao $BD$ và $CE$ cắt nhau tại $H$. Chứng minh:
♑ Giải bài 71 trang 85 sách bài tập toán 8 – Cánh diều Cho hình thang $ABCD$, $AB//CD$, $\widehat{DAB}=\widehat{DBC},\frac{AB}{BD}=\frac{2}{5}$. Tính diện tích tam giác $BDC$, biết diện tích tam giác $ABD$ là $44,8c{{m}^{2}}$.
🎶 Giải bài 72 trang 85 sách bài tập toán 8 – Cánh diều Cho hình bình hành $ABCD\left( AC>BD \right)$. Vẽ $CE$ vuông góc với đường thẳng $AB$ tại $E,CF$ vuông góc với đường thẳng $AD$ tại $F,BH$ vuông góc với đường thẳng $AC$ tại $H$.

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Giải bài 67 trang 85 sách bài tập toán 8 – Cánh diều

Tham Gia Group Dành Cho Lớp 8 Chia Sẻ, Trao Đổi Tài Liệu Miễn Phí

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