Given ABCDEF express CD in terms of AB and BC
To express CD in terms of AB and BC, we can use the concept of similar triangles.
First, let's identify the triangles that we can work with. In the given figure ABCDEF, we can see that triangle ABC is similar to triangle CDE. Therefore, we can use the fact that corresponding sides of similar triangles are proportional.
Let's denote the lengths of the sides:
AB = a
BC = b
CD = x
Since triangles ABC and CDE are similar, we can set up the following proportion:
AB/BC = CD/DE
Plugging in the values, we get:
a/b = x/DE
Now, we need to find the length of DE in terms of AB and BC. We can use the fact that triangle ABC is similar to triangle DEF to find this relationship.
AB/BC = DE/EF
Plugging in the given values, we get:
a/b = DE/EF
Now, we can substitute the value of DE from the equation above into the previous proportion:
a/b = x/(AB/BC) * EF
Simplifying this expression, we have:
a/b = x * BC/AB * EF
To express CD in terms of AB and BC, we solve for x:
x = (a/b) * AB/BC * EF
Therefore, CD is equal to:
CD = (a/b) * AB/BC * EF