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Giải mục 1 trang 68, 69 SGK Toán 8 – Chân trời sáng tạo

Tứ giác

🍰Tổng hợp đề thi học kì 2 lớp 8 tất cả các môn - Chân trời sáng tạo

Toán - Văn - Anh - Khoa học tự nhiên
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HĐ 1

Video hướng dẫn giải

✤Tứ giác \(ABCD\) (Hình 1b) là hình vẽ minh họa một phần của chiếc thang ở Hình 1a. Nêu nhận xét của em về hai cạnh \(AB\) và \(CD\) của tứ giác này.

Phương pháp giải:

Quan sát, sử dụng kiến thức về hai đường thẳng song song

Lời giải chi tiết:

Hai cạnh \(AB\) và \(CD\) song song với nhau

TH 1

Video hướng dẫn giải

𓃲Tìm các góc chưa biết của hình thang \(MNPQ\) có hai đáy là \(MN\) và \(QP\) trong mỗi trường hợp sau.

🍸a) \(\widehat Q = 90^\circ \) và \(\widehat N = 125^\circ \)

b) \(\widehat P = \widehat Q = 110^\circ \)

Phương pháp giải:

Sử dụng kiến thức về hình thang, hình thang cân, hình thang vuông

Lời giải chi tiết:

🎃a) Hình thang \(MNPQ\) có \(\widehat Q = 90^\circ \) nên là hình thang vuông. Suy ra \(\widehat M = 90^\circ \)

ꩵÁp dụng định lí tổng các góc của một tứ giác, ta có: \(\widehat P = 360^\circ  - \left( {90^\circ  + 90^\circ  + 125^\circ } \right) = 55^\circ \)

⭕b) Hình thang \(MNPQ\) có \(\widehat P = \widehat Q = 110^\circ \) nên là hình thang cân.

ꦯSuy ra \(\widehat M = \widehat N = 180^\circ  - 110^\circ  = 70^\circ \)

VD 1

Video hướng dẫn giải

ꦅMột mặt tường của chân tháp cột cờ Hà Nội có dạng hình thang cân \(ABCD\) (hình 4). Cho biết \(\widehat D = \widehat C = 75^\circ \). Tìm số đo  \(\widehat A\) và \(\widehat B\).

Phương pháp giải:

Sử dụng định nghĩa hình thang cân.

Lời giải chi tiết:

💮Do ${ABCD}$ là hình thang cân (gt) nên \(\widehat A = \widehat B\)

♛Xét hình thang \(ABCD\) ta có: \(\widehat {\rm{A}} + \widehat {\rm{B}} + \widehat {\rm{C}} + \widehat {\rm{D}} = 360^\circ \)

🅷\(\begin{array}{l}\widehat A + \widehat B + 75^\circ  + 75^\circ  = 360^\circ \\\widehat A + \widehat B = 210^\circ \end{array}\)   

Mà \(\widehat A = \widehat B\) (cmt)

🅰Suy ra : \(\widehat {\rm{A}} = \widehat B = 105^\circ \)

VD 2

Video hướng dẫn giải

Tứ giác \(EFGH\) có các góc cho như trong Hình 5.

a) Chứng minh rằng \(EFGH\) là hình thang

b) Tìm góc chưa biết của tứ giác

Phương pháp giải:

a) Chứng minh \(EH\) // \(FG\)

b) Sử dụng định lý tổng bốn góc của tứ giác bằng \(360^0\)

Lời giải chi tiết:

a) Ta có:

𝕴\(\widehat {\rm{E}} + \widehat {\rm{F}} = 95^\circ  + 85^\circ  = 180^\circ \)

Mà hai góc ở vị trí trong cùng phía

Suy ra \(EH\;{\rm{//}}\;FG\)

Suy ra \(EFGH\) là hình thang

✨b) Xét hình thang \(EFGH\) ta có: \(\widehat E + \widehat F + \widehat G + \widehat H = 360^\circ \)

🐻\(\begin{array}{l}95^\circ  + 85^\circ  + 27^\circ  + \widehat H = 360^\circ \\\widehat H = 153^\circ \end{array}\)

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