Răspuns:
[tex]\color{blue}\Large \boxed{\bf BO= 5~cm}[/tex]
[tex]\color{red}\Large\boxed{\bf m(\measuredangle DAO)=55^{\circ}}[/tex]
Explicație pas cu pas:
TEORIE:
Rombul este paralelogramul cu 2 laturi consecutive congruente, așadar toate laturile sunt congruente.
Unghiurile rombului cele opuse sunt egale:
- [tex]\large\bf m(\measuredangle BCD)=m(\measuredangle DAB)[/tex]
- [tex]\large\bf m(\measuredangle ABC)=m(\measuredangle CDA)[/tex]
Diagonale:
se înjumătățesc: [tex]\bf AO \equiv OC, \ BO \equiv OD[/tex]
sunt perpendiculare
sunt bisectoarele unghiurilor
Laturile rombului sunt egale si cele opuse sunt paralele două câte două[tex]\large\bf AB \parallel CD,\ AD \parallel BC[/tex]
[tex]\large \bf AB = BC=CD=DA[/tex]
[tex]\large\bf AC, BD~ diagonale~rombui\implies AC = d_{1}~si ~BD = d_{2}[/tex]
[tex]\color{red}\large\boxed{ \bf Arie~romb=\dfrac{d_{1}\cdot d_{2}}{2}}[/tex]
[tex]\color{Purple}\large\boxed{\bf Perimetru ~romb=4\cdot \ell}[/tex]
===============================
[tex]\large\bf BD = 10~cm\implies \boxed{\bf BO=OD = 5~cm}[/tex]
[tex]\large\bf m(\measuredangle ABC)+m(\measuredangle BCD)+m(\measuredangle CDA)+m(\measuredangle DAB)=360^{\circ}[/tex]
[tex]\large\bf 70^{\circ}+m(\measuredangle BCD)+70^{\circ}+m(\measuredangle DAB)=360^{\circ}[/tex]
[tex]\large\bf 140^{\circ}+m(\measuredangle BCD)+m(\measuredangle DAB)=360^{\circ}[/tex]
[tex]\large\bf 2\cdot m(\measuredangle BCD)=360^{\circ}-140^{\circ}[/tex]
[tex]\large\bf 2\cdot m(\measuredangle BCD)=220^{\circ}~~\bigg|:2[/tex]
[tex]\large\boxed{\bf m(\measuredangle BCD)=m(\measuredangle DAB)=110^{\circ}}[/tex]
In romb diagonale sunt bisectoarele unghiurilor ⇒
[tex]\large\bf m(\measuredangle DAO)=m(\measuredangle DAB):2\implies m(\measuredangle DAO)=110^{\circ}:2\implies[/tex]
[tex]\color{red}\large\boxed{\bf m(\measuredangle DAO)=55^{\circ}}[/tex]
Bafta multa!
P.S.: Te rog sa glisezi spre stânga pentru a vedea toata rezolvarea daca esti pe telefon
==pav38==
