UNIT 6
Triangles
LESSON 10
The Pythagorean Theorem Portfolio
In this unit, we will explore the Pythagorean Theorem and its applications in solving problems related to triangles. We will also develop an understanding of the relationship between the sides and angles of right triangles.
This portfolio will serve as a collection of your work and understanding of the Pythagorean Theorem. You will complete a series of activities and exercises to demonstrate your knowledge and problem-solving skills.
Activity 1: Exploring the Pythagorean Theorem
In this activity, you will investigate the relationship between the sides of a right triangle using the Pythagorean Theorem. You will be given several right triangles with different side lengths, and you will use the theorem to determine the lengths of the missing sides.
Activity 2: Applications of the Pythagorean Theorem
In this activity, you will apply the Pythagorean Theorem to solve real-world problems. You will be given various scenarios that involve right triangles, and you will use the theorem to find missing side lengths or determine if a triangle is right.
Activity 3: Proofs of the Pythagorean Theorem
In this activity, you will explore different proofs of the Pythagorean Theorem. You will use geometric and algebraic methods to prove the theorem and gain a deeper understanding of its validity.
Activity 4: Pythagorean Triples
In this activity, you will investigate Pythagorean triples, which are sets of three positive integers that satisfy the Pythagorean Theorem. You will identify patterns and relationships between the numbers in these triples.
Exercise 1: Solve for the Missing Side
In this exercise, you will be given a right triangle with two known side lengths, and you will use the Pythagorean Theorem to find the length of the missing side. You will also determine if the triangle is acute, obtuse, or right.
Exercise 2: Word Problems
In this exercise, you will solve word problems that involve the Pythagorean Theorem. You will be given real-life scenarios, such as finding the height of a ladder against a wall or the distance between two points on a coordinate plane, and you will use the theorem to find the solution.
Exercise 3: Identifying Right Triangles
In this exercise, you will be given a set of triangles, and you will determine if each triangle is right. You will use the Pythagorean Theorem to check if the triangle satisfies the conditions of a right triangle.
By completing these activities and exercises, you will develop a strong understanding of the Pythagorean Theorem and its applications in solving problems related to triangles. You will also improve your problem-solving skills and gain confidence in working with right triangles.