a) Ta có:
\(\dfrac{AB}{DF}=\dfrac{6}{12}=\dfrac{1}{2}\)
\(\dfrac{AC}{EF}=\dfrac{9}{18}=\dfrac{1}{2}\)
\(\dfrac{BC}{DE}=\dfrac{12}{24}=\dfrac{1}{2}\)
\(\Rightarrow\dfrac{AB}{DF}=\dfrac{AC}{EF}=\dfrac{BC}{DE}=\dfrac{1}{2}\)
Xét \(\Delta ABC\) và \(\Delta FDE\) có:
\(\dfrac{AB}{DF}=\dfrac{AC}{EF}=\dfrac{BC}{DE}\) (cmt)
\(\Rightarrow\Delta ABC\sim\Delta FDE\) (c-g-c)
Do \(\dfrac{AB}{DF}=\dfrac{AC}{EF}\) (cmt)
\(\Rightarrow AB.EF=AC.DF\)
b) Chu vi \(\Delta ABC\)
\(P_1=AB+AC+BC=6+9+12=27\left(cm\right)\)
Chu vi \(\Delta FDE\):
\(P_2=DF+EF+DE=12+18+24=54\left(cm\right)\)
Tỉ số chu vi của chúng:
\(\dfrac{P_1}{P_2}=\dfrac{27}{54}=\dfrac{1}{2}\)
Cách 2 (không khuyến khích làm theo cách này):
a) Ta có:
AB . EF = 6 . 18 = 108 (cm)
AC . DF = 9 . 12 = 108 (cm)
\(\Rightarrow AB.EF=AC.DF=108\left(cm\right)\)
