A30 ◦C B60 ◦D30 ◦F E60 ◦G30 ◦K H60 ◦Dividing lengths of sides (ratios)
AB
BC=AB
AC=CB
AC=
DE
EF =DE
DF=F E
DF=
GH
HK=GH
GK=KH
GK=What observations can you make about the ratios of the sides?Have you noticed that it does not matter what the lengths of the sides of the triangles are, if the angle remains
constant, the ratio of the sides will always yield the same answer?In the triangles below,△ABCis similar to△DEF. This is written as:△ABCjjj△DEF
ABCDEFIn similar triangles, it is possible to deduce ratios between corresponding sides:
AB
BC=
DE
EF
AB
AC
=
DE
DF
AC
BC
=
DF
EF
AB
DE
=
BC
EF
=
AC
DF
Chapter 5. Trigonometry 109