a Let's begin by naming the triangles on the given diagram.
Recall that the area of a triangle is half of the product of its base and height. Keeping this in mind, we can conclude that 12ad is the area of â–ł ABE, where d is the base and a is the height. ALso, 12bc is the area of â–ł ACD, where b is the base and c is the height.
Notice that when we remove the area of â–ł ABE, triangle â–ł CBE remains and has a height of a and a base of b- d. Similarly, when we remove the area of â–ł ACD, triangle â–ł CBD remains and has a base of a and a height of b- d. By the formula for area of a triangle, the remaining triangles, â–ł CBD and â–ł CBE have the same area.
A=1/2a(b-d)
From here, we can finally conclude that 12ad= 12bc, and therefore, ad=bc.
1/2ad=1/2bc * 2 ⟶ ad=bc
m_l=rise/run
When we examine the figure, we see that there are two different ratios that represent the slope of l.
From point A to point D, the rise is c and the run is d. From point A to point B, the rise is a and the run is b.
m_l=c/d or m_l=a/b
By the Transitive Property of Equality, we can conclude that cd= ab. From here, we can show that ad=bc by multiplying each side by b and d.
c/d=a/b → ad=bc
