Question

[Huỳnh Thiên Tân]

Vì \(EI//AB\)và \(AB//DM\Rightarrow EI//DM\)  nên \(\frac{AE}{AD}=\frac{AI}{IM}=\frac{EI}{DM}\left(1\right)\)

Vì \(AB//MC\) và \(KF//AB\Rightarrow KF//MC\Rightarrow\frac{BK}{BM}=\frac{BF}{BC}=\frac{KF}{MC}\left(2\right)\)

Ta có : IK // AB \(\Rightarrow\frac{AI}{AM}=\frac{BK}{BM}\left(3\right)\)

Từ(1) (2)(3), \(\Rightarrow\frac{EI}{DM}=\frac{KF}{MC}\)

Mà DM=MC => EI=KF \(\left(\cdot\right)\)

Ta có : \(IK//DM\Rightarrow\frac{IK}{DM}=\frac{IB}{BD}=\frac{BK}{BM}\left(4\right)\)

Ta có : EI // AB

\(\Rightarrow\frac{IB}{BD}=\frac{AE}{AD}\left(5\right)\)

Từ (1)(4)(5) \(\Rightarrow\frac{EI}{DM}=\frac{IK}{DM}\Rightarrow EI=IK\left(\cdot\cdot\right)\)

Từ \(\left(\cdot\right)\left(\cdot\cdot\right)\Rightarrow EI=IK=KF\)