a Create a proportion using proportional parts of triangles.
B
b Solve a proportion you found in the previous part using cross products.
A
aExample Solution: 6/4=x-2/5
B
b x=9.5, AB=7.5
Practice makes perfect
a Let's begin with recalling that if there are segments created by a line parallel to one side of a triangle and intersecting the other two sides, then the corresponding parts of these sides are proportional.
In our exercise DE is parallel to one side of △ ABC and intersects the other two sides. Therefore, we can create a proportion using the fact that corresponding parts of BA and BC are proportional. Notice that BD is 6, as it is the difference between the lengths of AB and DA.
BD/DA=BE/EC ⇒
6/4=x-2/5
Notice that this is only one of the possible solutions.
b Now, we will find the value of x by solving a proportion we found in the previous part. We will start with cross multiplication. Remember to treat x-2 like a single term.
