In this section the Triangle Proportionality Conjecture is explored using geometric interactive applets.

There is a relationship between angles and their opposite sides. Opposite means located directly across from something else. Look at the triangle and identify the opposites by clicking on the angle to highlight the opposite side.

In the page linked below, click on and drag the orange dot at vertex A to change the value of vertex A.

Interior Angles of a Triangle

While dragging vertex A around the screen, observe the change in the angle and side measurements.

Write your observations and answers to the following questions questions in your notes.

• As the value of A increases, what happens to the other two angles and the two adjoining sides?
• As the value of A decreases, what happens to the other two angles and the two adjoining sides?
• What is the relationship between the angles and their opposite sides?
• Which angle and side is the largest? Smallest?

After experimenting with the diagram, click on the four correct statements/conjectures below.

Correct answers will remain bold.

Review the correct statements/conjectures. Write a statement describing your conclusion.

Interactive popup. Assistance may be required. Check Your Answer The Triangle Proportionality Property: In every triangle the longest side is opposite the largest angle, and the shortest side is opposite the smallest angle.