Question

Answer 1

1) \(\dfrac{MI}{AB}=\dfrac{DI}{DB}=\dfrac{CN}{CB}\)

2) \(\dfrac{MI}{AB}=\dfrac{CN}{CB}=\dfrac{IN}{AB}\)

Answer 2

1: Xét ΔDAB có MI//AB

nên \(\dfrac{MI}{AB}=\dfrac{DM}{DA}\left(1\right)\)

Xét ΔCBA có IN//AB

nên \(\dfrac{CN}{CB}=\dfrac{IN}{AB}\)(2)

Xét hình thang ABCD có MN//AB//CD

nên \(\dfrac{AM}{MD}=\dfrac{BN}{NC}\)

=>\(\dfrac{AM+MD}{MD}=\dfrac{BN+NC}{NC}\)

=>\(\dfrac{AD}{DM}=\dfrac{BC}{NC}\)

=>\(\dfrac{DM}{DA}=\dfrac{CN}{CB}\left(3\right)\)

Từ (1),(2),(3) suy ra \(\dfrac{MI}{AB}=\dfrac{CN}{AB}=\dfrac{IN}{AB}\)

2: Ta có: \(\dfrac{MI}{AB}=\dfrac{IN}{AB}\)

=>MI=IN