Triangle Proportionality Theorems WS

Use this applet to discover the triangle proportionality theorem!

Task 1:

Let's explore proportions within triangles. Click and drag the vertices of triangle ABC below to create different triangles. Play around with it a bit. Watch the proportions change. Toggle the side lengths and ratios on. You will need these for the next few questions.

Task 2:

Drag your vertices to create your first triangle. What are the lengths of AE, EB, AD, and DC respectively? (Separate your responses with a comma)

What are the ratios of AE:EB and AD:DC respectively? (Separate your responses with a comma)

Task 3:

Drag the vertices again to create your second triangle. What are the lengths of AE, EB, AD, and DC respectively? (Separate your responses with a comma)

Now, what are the ratios of AE:EB and AD:DC respectively? (Separate your responses with a comma)

Question 1:

What do you notice about the ratios in Task 1? What do you notice about the ratios in Task 2?

Question 2:

What do you notice about the relationship between line segment ED and line segment BC in each of your triangles?

Question 3:

Make a conjecture about what happens whenever you draw a line parallel to one side of a triangle. Do you think this always occurs? Explain.

Apply What You've Learned

Figure 1

Question 4:

Applying what you saw in Tasks 1-3, calculate the length of segment HC in figure 1. Think about the proportion you could set up to help you find it.

Figure 2

Question 5:

What is the length of segment CE in figure 2? Use a similar proportion to the proportion in Question 4.

Question 6:

What do you notice about the situation above? What is proportional? What is the relationship between lines AB, CE, and FD?

Figure 3

Find the length of QN using what you saw in Question 6.