Progression of Skills - Similarity, Right Triangles, and Trigonometry

Before this lesson:

 Students should be fluent in the Pythagorean theorem and have a basic understanding of the difference between congruence and similarity. For example,  if a student can complete these activities with little to no help, they are ready for this toolkit! 

• Pythagorean Theorem Activity
• Congruent & Similar Triangle Activity 
• Similarity Triangle Activity
• Similarity Versus Congruence Triangles

Students Do:

Students will be able to explain how to find the heights of tall objects 
(such as buildings and lamp posts) using similar triangles and the Pythagorean theorem.

This Toolkit Lesson:

 Focuses on congruent and similar triangles to solve multi-step word problems with multiple methods for solving, using proofs and using the Pythagorean theorem to find missing lengths.

Students Do:

Students will be able to explain how to find the length of a building using similar triangles and the Pythagorean theorem.

After this lesson:

Students should practice finding missing sides of similar triangles or finding the heights of large buildings. There are many examples identified at the end of this toolkit that would be useful to try, like finding the width of a river or the height of a tree! 

Students Do:

Students standing at a certain distance from a tall building measure their own height, the angle of elevation, and the building's shadow length to set up a proportion and calculate the building's height to be 7.5 meters