Theory:

1. In isosceles Trapezium, angles that are adjacent to the base have equal measures.

2. Diagonals of isosceles Trapezium has equal length.

$$AC = BD$$.

Characterizations of isosceles Trapezium :
1. If angles adjacent to the base have equal measures, then the Trapezium is isosceles trapezium.
2. If diagonals of trapezium have equal lengths, then the Trapezium is isosceles trapezium.