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Giải bài 3.10 trang 56 SGK Toán 8 tập 1 - Kết nối tri thức

Cho hình thang cân ABCD (AB // CD) có AB = AD.

ꦅTổng 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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Đề bài

🌃Cho hình thang cân ABCD (AB // CD) có AB = AD. Biết \(\widehat {AB{\rm{D}}} = {30^o}\), tính số đo các góc của hình thang đó.

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

Áp dụng định lí tổng các góc trong một tứ giác bằng \(360^0\)

Lời giải chi tiết

Xét tam giác ABD cân tại A (vì AB = AD), ta có: • \(\widehat {AB{\rm{D}}} = \widehat {A{\rm{D}}B} = {30^o}\) • \(\widehat A + \widehat {AB{\rm{D}}} + \widehat {A{\rm{D}}B} = {180^o}\) hay \(\widehat A + {30^o} + {30^o} = {180^o}\)

Suy ra \(\widehat A\)=180°−30°−30°=120o

Vì AB // CD nên \(\widehat {A{\rm{B}}D} = \widehat {B{\rm{D}}C} = {30^o}\) (hai góc so le trong). Do đó \(\widehat {ADC} = \widehat {A{\rm{D}}B} + \widehat {C{\rm{D}}B}\)=30°+30°=60° Vì tứ giác ABCD là hình thang cân nên \(\widehat {ADC} = \widehat C\)=60° Ta có: \(\widehat A + \widehat {ABC} + \widehat C + \widehat {A{\rm{D}}C} = {360^o}\) 120°+60°+60°+\(\widehat {A{\rm{B}}C}\)=360° 240°+\(\widehat {A{\rm{B}}C}\)=360° Suy ra =360°−240°=120° Vậy số đo các góc của hình thang ABCD là \(\widehat A = {120^o};\widehat {ABC} = {120^o};\widehat {C} = {60^o};\widehat {A{\rm{D}}C} = {60^o}\).

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