So the e coordinate is (3,0)
The slope of the straight line AB =(3-0)/(0+ 1)=3.
The slope of the straight line BE =(3-0)/(0-3)=- 1.
The slope of the straight line BD =(3-4)/(0- 1)= 1.
The slope of the straight line DE =(4-0)/( 1-3)=-2.
So BE⊥BD, so △DEB is a right triangle.
Because △AOB is a right triangle
Therefore, only right triangles are similar to them.
That is, △EOB and △DEB may be similar to △AOB.
AO= 1,BO=3,OE=3,BD=√2,BE=3√2。
So AO:BO= 1:3.
BO:EO= 1: 1
BD:BE=√2:3√2= 1:3
So △DEB is similar to △AOB.