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Giải mục 2 trang 113, 114 SGK Toán 8 tập 1 - Cánh diều

Cho hình thoi ABCD có hai đường chéo là AC và BD cắt nhau tại O (hình 58) a) Hình thoi ABCD có là hình bình hành hay không? b) Hai đường chéo AC và BD có vuông góc với nhau hay không? c) Hai tam giác ABC và ADC có bằng nhau hay không? Tia AC có phải là tia phân giác của (widehat {BA{rm{D}}}) hay không?

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

Toán - Văn - Anh - Khoa học tự nhiên
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HĐ2

Video hướng dẫn giải

Cho hình thoi ABCD có hai đường chéo là AC và BD cắt nhau tại O (hình 58)

a) Hình thoi ABCD có là hình bình hành hay không? b) Hai đường chéo AC và BD có vuông góc với nhau hay không? c) Hai tam giác ABC và ADC có bằng nhau hay không? Tia AC có phải là tia phân giác của \(\widehat {BA{\rm{D}}}\) hay không?

Phương pháp giải:

Quan sát hình và chứng minh các tam giác tương ứng bằng nhau

Lời giải chi tiết:

a) Hình thoi ABCD có là hình bình hành (vì AB = BC = CD = DA) b) Xét tam giác ABD có AB = AD nên tam giác ABD là tam giác cân tại A. Suy ra đường trung tuyến AO đồng thời là đường cao. Suy ra AO vuông góc với BD Hay AC vuông góc với BD c) Xét tam giác ABC và tam giác ADC có: AD = AB CD = CB AC chung \(\begin{array}{l}\Delta ABC = \Delta A{\rm{D}}C\\ \Rightarrow \widehat {DAC} = \widehat {BAC}\end{array}\)

Mà AC  nằm giữa 2 tia AB và AD

Suy ra: AC là tia phân giác của góc BAD

LT1

Video hướng dẫn giải

Cho hình thoi ABCD có \(\widehat {ABC} = {120^o}\). Chứng minh tam giác ABD là tam giác đều.

Phương pháp giải:

Vận dụng các tính chất của hình thoi: chứng minh tam giác ABD cân tại A và có \(\widehat A = {60^o}\)

Lời giải chi tiết:

Vì ABCD là hình thoi Suy ra: \(\widehat B = \widehat D = {120^o}\) Mà: \(\widehat A = \widehat C\) Mặt khác: \(\widehat A + \widehat B + \widehat C + \widehat D = {360^o}\) Suy ra: \(\widehat A = \widehat C = \dfrac{{{{360}^o} - \widehat B - \widehat D}}{2} = \dfrac{{{{360}^o} - {{120}^o} - {{120}^o}}}{2} = {60^o}\) Xét tam giác ABD có AB = AD nên tam giác ABD là tam giác cân tại A mà \(\widehat A = {60^o}\) Suy ra tam giác ABD là tam giác đều

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