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theo bài ra ta có hình vẽ :
O x z t y
a) & b) Vì Oz là tia phân giác của \(\widehat{xOy}\)
=> \(\widehat{xOz}\)= \(\widehat{zOy}\)= \(\frac{\widehat{xOy}}{2}\)= \(50^o\)
Vì \(\widehat{yOt}\)< \(\widehat{yOz}\)( \(25^o< 50^o\)) nên tia Ot nằm giữa hai tia Oz và Oy
\(\Rightarrow\widehat{yOt}+\widehat{tOz}=\widehat{yOz}\)
hay \(25^o+\widehat{tOz}=50^o\)
\(\Rightarrow\widehat{tOz}=50^o-25^o=25^o\)
Vì \(\widehat{yOt}=\widehat{tOz}=\widehat{\frac{yOz}{2}}=\frac{50^o}{2}=25^o\)và Ot nằm giữa hai tia Oz và Oy
=> Ot là tia phân giác của \(\widehat{yOz}\)
Bài 2:
\(a.\)Vì \(\widehat{xOy}\)kề bù với góc \(\widehat{yOz}\)\(\Rightarrow\)\(\widehat{xOy}+\widehat{yOz}=180^0\)
\(\Rightarrow\) \(60^0+\widehat{yOz}=180^0\)
\(\Rightarrow\) \(\widehat{yOz}=180^0-60^0=120^0\)
\(b.\) Vì \(Ot\)là tia phân giác \(\widehat{xOy}\)\(\Rightarrow\)\(\widehat{tOy}=\frac{\widehat{xOy}}{2}=\frac{60^0}{2}=30^0\)
Vì \(Om\)là tia phân giác \(\widehat{yOz}\)\(\Rightarrow\)\(\widehat{yOm}=\frac{\widehat{yOz}}{2}=\frac{120^0}{2}=60^0\)
Vì \(Oy\)nằm giữa 2 tia \(Ot\)và \(Om\) \(\Rightarrow\) \(\widehat{tOy}+\widehat{yOm}=\widehat{tOm}\)
\(\Rightarrow\) \(30^0+60^0=\widehat{tOm}\)
\(\Rightarrow\) \(90^0=\widehat{tOm}\)
Vậy \(\widehat{tOm}\)là góc vuông
Bài 2: Vì góc xOy và yoz kề bù nên góc xOz= 180 độ Ta có : Góc xoy + góc yoz = xOz Hay : 60 độ + góc yoz = 180 độ góc yoz = 180 độ - 60 độ = 120 độ Vậy....
vì góc xOy và yOz là 2gocs kề bù vì tia ot là tia phân giác của yOz nênyOt=tOz=yOz/2=120/2=60
Nên xOy+yOz=180 góc xOy và yOz là 2 góc kề bù mà tia ot là tia phân giác của yOz
nên tia oy nằm giữa tiaox,ot
60+yOz=180 vậy tia oy là tia phân giác của góc zOt vì+tia oy nằm giữa oz,oz
yOz=180-60=120 +yOt=xOy=60
Vẽ hình bn tự vẽ nha....
a, Có góc xOy và góc yOz là 2 góc kề bù nên suy ra xOy+yOz=180 độ
60+yOz=180(vì xOy=60)
yOz=180-60
yOz=120
Vậy góc yOZ bằng 120 độ
Đề bài sai à bạn? S k vẽ hình đc câu b vậy?
Bạn tự vẽ hình nhà!
a,Vì hai goc xOy và yOz là hai góc kè bù.
=> xOy+yOz=180
hay 120+yOz=180
=> yOz=180-120
=> yOz=60
a) Góc \(\widehat{xOt}\)kề bù với \(\widehat{yOt}\)nên:
\(\widehat{xOt}=180^o+\widehat{yOt}=180^o-60^o=120^o\)
Trên cùng nửa mặt phẳng bờ chứa tia Ox có: \(\widehat{xOz}< \widehat{xOt}\)
=> Tia Oz nằm giữa 2 tia Ox và Ot
b) Có tia Oz nằm giữa 2 tia Ox và Ot
=> \(\widehat{xOz}+\widehat{zOt}=\widehat{xOt}\)
=> \(\widehat{tOz}=\widehat{xOt}-\widehat{xOz}=120^o-40^o=80^o\)
c) Nếu \(\alpha+\beta=180^o\)thì \(\widehat{zOt}=180^o-\left(\alpha+\beta\right)\)
Nếu \(\alpha+\beta>180^o\)thì \(\widehat{zOt}=\left(\alpha+\beta\right)-180^o\)
a) Trên cùng một nửa mặt phẳng bờ chứa tia Ox, ta có : \(\widehat{xOy}< \widehat{xOz}\left(70^o< 140^o\right)\)
=> Tia Oy nằm giữa hai tia Ox và Oz
\(\Rightarrow\widehat{xOy}+\widehat{yOz}=\widehat{xOz}\)
\(\Rightarrow70^o+\widehat{yOz}=140^o\)
\(\Rightarrow\widehat{yOz}=140^o-70^o\)
\(\Rightarrow\widehat{yOz}=70^o\)
b) Vì tia Ot là tia đối của tia Oz
\(\Rightarrow\widehat{zOt}=180^o\)
Trên cùng một nửa mặt phẳng bờ chứa tia Ox, ta có : \(\widehat{yOz}< \widehat{zOt}\left(70^o< 180^o\right)\)
=> Tia Oy nằm giữa hai tia Ot và Oz
\(\Rightarrow\widehat{zOy}+\widehat{yOt}=\widehat{zOt}\)
\(\Rightarrow70^o+\widehat{yOt}=180^o\)
\(\Rightarrow\widehat{yOt}=180^o-70^o\)
\(\Rightarrow\widehat{yOt}=110^o\)
chú ý phải làm dài
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
ez :>
x O y z t
a) vì \(\widehat{xOy}\)kề bù với \(\widehat{yOz}\)
\(\Rightarrow\widehat{xOy}+\widehat{yOz}=\widehat{xOz}=180^o\)
\(\Rightarrow30^o+\widehat{yOz}=180^o\Leftrightarrow\widehat{yOz}=180^o-30^o=150^o\)
b) vì \(\widehat{zOt}< \widehat{zOy}\left(60^o< 150^o\right)\)
suy ra tia Ot nằm giữa hai tia Oy và Oz
\(\Rightarrow\widehat{zOt}+\widehat{yOt}=\widehat{zOy}\)
\(\Rightarrow60^o+\widehat{yOt}=150^o\Leftrightarrow\widehat{yOt}=150^o-60^o=90^o\)
\(\Rightarrow Oy\perp Ot\left(đpcm\right)\)
Bài làm :
Ta có hình vẽ :
x O z y t
a)Vì góc xOy và góc yOz là 2 góc kề bù nên ta có :
\(\widehat{xOy}+\widehat{yOz}=180^o\)
\(\Rightarrow\widehat{yOz}=180-\widehat{xOy}=180-30=150^o\)
b) Ta có :
\(\widehat{yOt}+\widehat{tOz}=\widehat{yOz}=150^o\)
\(\Rightarrow\widehat{yOt}=\widehat{yOz}-\widehat{tOz}=150-60=90^0\)
Góc yOt = 90 độ => Oy vuông góc Ot
=> Điều phải chứng minh
Chúc bạn học tốt !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
":"||||||||||||||||||||||||||||||||||||||||/*//*//
x O y z t
a, Vì góc yOz kề bù với góc xOy nên :
góc yOz + góc xOy = 180độ
=> góc yOz = 180độ - góc xOy
=> góc yOz = 180độ - 30độ
=> góc yOz = 150độ
Vậy góc yOz = 150độ
b, Vì tia Ot nằm giữa hai tia Oz và Oy nên ta có :
góc zOt + góc yOt = góc yOz
=> 60độ + góc yOt = 150độ
=> góc yOt = 150độ - 60độ
=> góc yOt = 90độ
Suy ra : Oy vuông góc với Ot .
Học tốt
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