Theorems:
Two triangles are said to similar if,
1)Their corresponding angles are equal.
2)Their corresponding sides are proportional.
Corresponding angles:
In two similar triangles, angles which are equal are called corresponding angles.
If, \[ \Delta ABC\approx \Delta DEF\]
\[\frac{AB}{DE}=\frac{BC}{EF}=\frac{CA}{FD}\]
\[\therefore \angle A=\angle D\] as they are opposite to corresponding sides BC and EF respectively.
Similarly \[\angle B=\angle E\] and \[\angle C=\angle F\].
Corresponding sides:
In similar triangles, sides opposite to equal angles are known as corresponding sides and they are in a proportion.
In the figure, \[\angle A=\angle D\] , \[\angle B=\angle E\] , \[\angle C=\angle F\] .
\[\therefore AB and DE\] are corresponding sides as they are opposite to the equal angles \[\angle Cand\angle F\] respectively.
Similarly, BC and EF are corresponding sides as they are opposite to \[\angle A and \angle D\] respectively and CA and FD are corresponding sides as they are opposite to \[\angle B and \angle E\] respectively.
Thus, \[\frac{AB}{DE}=\frac{BC}{EF}=\frac{CA}{FD}\] are corresponding ratios between sides of similar triangles which are in a proportion.
