## Clarifying the Learning

### Lesson Overview

In this lesson you will prove the Pythagorean Theorem, derive the Distance Formula using the Pythagorean Theorem, and solve real-world applications involving the Pythagorean Theorem. The Pythagorean Theorem is one of the most widely used mathematical principles in the real world; its applications are numerous. Using the Pythagorean Theorem is simple—it is a concept that is taught to students at an early age. Understanding where the Pythagorean Theorem comes from and how it can be used to derive the Distance Formula are also necessary in order to use it in a variety of situations. In today’s lesson, we are going to look at the Pythagorean Theorem and its converse, the Distance Formula, and the Midpoint Formula.

### Driving Question

Why is the Pythagorean Theorem important, and how is it used to solve real world situations?

## Defining Success

### Content Standards and Objectives:

After completing this lesson, you should be able prove theorems about triangles (including theorems involving the Pythagorean Theorem and its converse and proportionality when a segment parallel to a side of the triangle exists in its interior).**(M.2HS.STP.7)(CCSS.Math.Content.HSG-SRT.B.4)**

Upon mastering this objective, you should be able to conduct the tasks in the video below: