After learning many different strategies for solving triangles in unit 3, we are ready to start talking about similar triangles. Similar triangles are created when a dilation is performed on an original triangle. We would say that the original triangle and the copy triangle (image) are both similar figures. Can you remember dilations from way back in unit 1?
In this unit we will discover what a triangle similarity statement is and exactly how it can be used to solve problems involving similar triangles. Given that two triangles are similar, students will be able to set-up proportions and solve for missing side lengths.
After learning to problem solve in triangles, we will look at how to prove that two triangles are similar. Students will be given specific information about two triangles and will eventually be able to prove whether or not the two triangles are similar. We will do this using two-column proofs.
After similarity, students will learn what it means for two triangles to be congruent. Students will learn the shortcuts to proving triangle congruency, then will apply these using two-column proofs in order to show that two triangles are congruent.