Lesson: Parallel Lines in a Triangle Mathematics

In this lesson, we will learn how to find missing lengths in a triangle containing two or three parallel lines using proportionality.

Lesson Plan

Students will be able to

recognize when parallel lines inside or outside triangles create similar triangles (sometimes called the side splitter theorem),
use proportionality to find unknown lengths in triangles containing parallel lines,
solve multistep problems involving triangles containing parallel lines,
prove that a straight line is parallel to one side of a triangle due to having proportional parts (the inverse of the theorem).

Q1:

Using the diagram, which of the following is equal to ?

Q2:

Find the value of .

Q3:

In the figure, and are parallel. If , , and , what is the length of ?