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Thử tài bạn trang 112 Tài liệu dạy – học Toán 7 tập 2

Giải bài tập Điền vào chỗ trống để hoàn thành phần chứng minh định lí đảo.
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Đề bài

Điền vào chỗ trống để hoàn thành phần chứng minh định lí đảo.

 

Chứng minh: Xét hai trường hợp: * \(D \in AB\) (hình 45a): Vì DA = DB (gt) Nên D là………….của đoạn thẳng AB, do đó D thuộc…………của đoạn thẳng AB. * \(D \notin AB\)(hình 45b): Kẻ đoạn thẳng nối D với trung điểm I của đoạn thẳng AB. Ta có \(\Delta DAI = \Delta DBI\,\,\left( {c.c.c} \right)\) Suy ra \(\widehat {{I_1}} = ...........\) Mặt khác: \(\widehat {{I_1}} + \widehat {{I_2}} = {180^o}\,\,\left( {........} \right)\)

Nên ……………..=………….= 90o

Vậy………..là đường trung trực của đoạn thẳng AB.

Lời giải chi tiết

Chứng minh:

* \(D \in AB\) (hình 45a). Vì DA = DB (gt)Nên D là trung điểm của đoạn thẳng AB, do đó D thuộc đường trung trực của đoạn thẳng AB.* \(D \notin AB\) (hình 45b). Kẻ đoạn thẳng nối D với trung điểm của đoạn thẳng AB.Ta có \(\Delta DAI = \Delta DBI\,\,\left( {c.c.c} \right)\) \( \Rightarrow {\widehat I_1} = {\widehat I_2}.\)Mặt khác: \({\widehat I_1} + {\widehat I_2} = {180^o}\) (hai góc kề bù). Nên \({\widehat I_1} = {\widehat I_2} = 90^\circ .\)Vậy DI là đường trung trực của đoạn thẳng AB.

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