Question

va rog ajutor la ex 4 doar b si c​

Answer 1

b)

AE = 4; AB = 16, AC = 20, FC = 15

AF = AC-FC = 20-15 = 5

$\left.\begin{matrix} \dfrac{AE}{AB} = \dfrac{4}{16} = \dfrac{1}{4} \\ \\ \dfrac{AF}{AC} = \dfrac{5}{20} = \dfrac{1}{4}\end{matrix}\right\} \implies \dfrac{AE}{AB} = \dfrac{AF}{AC}$

$\implies EF ||BC$

c)

AB = 28, EB = 21, AF = 6, FC = 18

AE = AB-EB = 28-21 = 7

AC = AF+FC = 6+18 = 24

$\left.\begin{matrix} \dfrac{AE}{AB} = \dfrac{7}{28} = \dfrac{1}{4} \\ \\ \dfrac{AF}{AC} = \dfrac{6}{24} = \dfrac{1}{4}\end{matrix}\right\} \implies \dfrac{AE}{AB} = \dfrac{AF}{AC}$

$\implies EF ||BC$

q.e.d.