# Lesson 6

A Proof of the Pythagorean Theorem

Let’s prove the Pythagorean Theorem.

### Problem 1

1. Find the lengths of the unlabeled sides.
2. One segment is $$n$$ units long and the other is $$p$$ units long. Find the value of $$n$$ and $$p$$. (Each small grid square is 1 square unit.)

### Problem 2

Use the areas of the two identical squares to explain why $$5^2+12^2=13^2$$ without doing any calculations.

### Problem 3

Find the exact value of each variable that represents a side length in a right triangle.

### Problem 4

Write each expression as a single power of 10.

1. $$10^5 \boldcdot 10^0$$
2. $$\frac{10^9}{10^0}$$
(From Unit 7, Lesson 4.)

### Problem 5

Here is a scatter plot of weight vs. age for different Dobermans. The model, represented by $$y = 2.45x + 1.22$$, is graphed with the scatter plot. Here, $$x$$ represents age in weeks, and $$y$$ represents weight in pounds.

1. What does the slope mean in this situation?
2. Based on this model, how heavy would you expect a newborn Doberman to be?
(From Unit 5, Lesson 21.)