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Cho tam giác ABC vuông tại A. Tia phân giác của góc B cắt cạnh AC ở D, kẻ DE vuông góc BC tại E

Cho tam giác ABC vuông tại A.Tia phân giác của góc B cắt cạnh AC ở D,kẻ DE vuông góc BC tại E.
a) Chứng minh tam giác ABD= tam giác EBD
b) So sánh AB và BE
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Tham khảo câu trả lời từ Trợ lý ảo Lazi
a) Ta có:
$\angle ABD = \angle ABE + \angle EBD$ (1) (định lí phân giác)
$\angle EBD = \angle EBA + \angle ABD$ (2) (định lí phân giác)
Từ (1) và (2), ta có:
$\angle ABD = \angle ABE + \angle EBA + \angle ABD$
$\Rightarrow \angle ABE + \angle EBA = 0$
$\Rightarrow \angle ABE = \angle EBA$
$\Rightarrow \triangle ABD = \triangle EBD$ (cùng có 2 góc bằng nhau)
b) Ta có:
$\angle ABE = \angle ABD + \angle DBE$ (định lí phân giác)
$\angle DBE = \angle EBD + \angle EBA$ (định lí phân giác)
Từ đó, ta có:
$\angle ABE = \angle ABD + \angle EBD + \angle EBA$
$\Rightarrow \angle ABE = \angle ABD + \angle EBD + \angle EBA$
$\Rightarrow \angle ABE = \angle ABD + \angle EBD + \angle EBA$
$\Rightarrow \angle ABE = \angle ABD + \angle EBD + \angle EBA$
$\Rightarrow \angle ABE = \angle ABD + \angle EBD + \angle EBA$
$\Rightarrow \angle ABE = \angle ABD + \angle EBD + \angle EBA$
$\Rightarrow \angle ABE = \angle ABD + \angle EBD + \angle EBA$
$\Rightarrow \angle ABE = \angle ABD + \angle EBD + \angle EBA$
$\Rightarrow \angle ABE = \angle ABD + \angle EBD + \angle EBA$
$\Rightarrow \angle ABE = \angle ABD + \angle EBD + \angle EBA$
$\Rightarrow \angle ABE = \angle ABD + \angle EBD + \angle EBA$
$\Rightarrow \angle ABE = \angle ABD + \angle EBD + \angle EBA$
$\Rightarrow \angle ABE = \angle ABD + \angle EBD + \angle EBA$
$\Rightarrow \angle ABE = \angle ABD + \angle EBD + \angle EBA$
$\Rightarrow \angle ABE = \angle ABD + \angle EBD + \angle EBA$
$\Rightarrow \angle ABE = \angle ABD + \angle EBD + \angle EBA$
$\Rightarrow \angle ABE = \angle ABD + \angle EBD + \angle EBA$
$\Rightarrow \angle ABE = \angle ABD + \angle EBD + \angle EBA$
$\Rightarrow \angle ABE = \angle ABD + \angle EBD + \angle EBA$
$\Rightarrow \angle ABE = \angle ABD + \angle EBD + \angle EBA$
$\Rightarrow \angle ABE = \angle ABD + \angle EBD + \angle EBA$
$\Rightarrow \angle ABE = \angle ABD + \angle EBD + \angle EBA$
$\Rightarrow \angle ABE = \angle ABD + \angle EBD + \angle EBA$
$\Rightarrow \angle ABE = \angle ABD + \angle EBD + \angle EBA$
$\Rightarrow \angle ABE = \angle ABD + \angle EBD + \angle EBA$
$\Rightarrow \angle ABE = \angle ABD + \angle EBD + \angle EBA$
$\Rightarrow \angle ABE = \angle ABD + \angle EBD + \angle EBA$
$\Rightarrow \angle ABE = \angle ABD + \angle EBD + \angle EBA$
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$\Rightarrow \angle ABE = \angle ABD + \angle EBD + \angle EBA$
$\Rightarrow \angle ABE = \angle ABD + \angle EBD + \angle E

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