In this topic, you will learn how to describe some of the relationships that exist between the sides and angles of a triangle. For example, the measures of the angles of a triangle can give you insight into the side lengths of a triangle. By the end of this topic, you will know how to order the sides of a triangle when given only its angle measures. You will also know how to order the angles of a triangle when given only its side lengths.

Essential Questions

• How can you order the sides of a triangle when given its angle measures?
• How can you order the angles of a triangle when given its side lengths?

 

Warm-Up

Look at the following angles.

Notice that ∠DEF is larger than ∠ABC. Consider this: What if, for each angle, you sketched a third segment from D to F and from A to C? Which segment would you expect to be longer: line DF or line AC?

Could this have anything to do with the fact that m∠DEF is larger than m∠ABC?