Unghiurile ∢AOB și ∢BOC sunt adiacente suplementare, iar OM, respectiv ON, sunt bisectoarele acestora. Fie BD ⊥ OM, D ∈ OM și BE ⊥ ON, E ∈ ON . Demonstrați că: a) patrulaterul BDOE este dreptunghi. b) OB ≡ DE .

Answer:

Following are the solution to this question:

Step-by-step explanation:

[tex]\angle AOB + \angle BOC = 180\\\\\angle MON = (\angle AOB + \angle BOC): 2 \\\\[/tex]

            [tex]= 180: 2 \\\\=\frac{180}{2}\\\\= 90^{\circ}[/tex]

In point a:

[tex]\angle AOB = 60\\\\ \angle BOC = 120\\\\ \angle MON = (60 + 120): 2 \\\\[/tex]

            [tex]= 180: 2 \\\\=\frac{180}{2}\\\\= 90^{\circ}[/tex]

In point b:

[tex]\angle BOC = 100\\\\\angle AOB = 80\\\\ \angle MON = (100 + 80): 2[/tex]

            [tex]= 180: 2 \\\\=\frac{180}{2}\\\\= 90^{\circ}[/tex]

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A
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B
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C
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D
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