Răspuns:
ex.16) b || a
Explicație pas cu pas:
m(∢CAB) + m(∢DAB) = 180°
[tex]\frac{m( \angle CAB)}{2} = \frac{m(\angle DAB)}{7} = \frac{m(\angle CAB) + m(\angle DAB)}{2 + 7} = \frac{180 \degree}{9} = 20 \degree \\ [/tex]
[tex]m(\angle CAB) = 2 \times 20 \degree = 40 \degree \\ m(\angle DAB) = 7 \times 20 \degree = 140 \degree [/tex]
[AM este bisectoare => m(∢BAM) ≡ m(∢DAM)
=> m(∢DAM) = ½×m(∢DAB) = ½×140° = 70°
m(∢DAM) = m(∢AMB) = 70°
=> m(∢DAM) ≡ m(∢AMB) (alterne interne)
=> b || a
q.e.d.
