unit 9 lesson 1 homework (the pythagorean theorem) answer key

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Geometry (all content)

Course: geometry (all content)   >   unit 9.

• Unit test Pythagorean theorem

Unit 9 Lesson 1 Homework (The Pythagorean Theorem)

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• → 8th Grade

The Pythagorean Theorem Lesson Plan

Get the lesson materials.

The Pythagorean Theorem Guided Notes with Doodles Legs Hypotenuse Right Triangle

Ever wondered how to teach the Pythagorean Theorem in an engaging way to your 8th grade students?

In this lesson plan, students will learn about the Pythagorean Theorem proofs, legs and hypotenuse, right triangles, and their real-life applications. Through artistic, interactive guided notes, check for understanding, a color by code activity, and a real-life application example, students will gain a comprehensive understanding of the Pythagorean Theorem.

The lesson culminates with an exploration of baseball diamond highlighting the importance of understanding the Pythagorean Theorem in real-world scenarios.

• Type : Lesson Plans
• Grade : 8th Grade
• Standard : CCSS 8.G.B.7

Learning Objectives

After this lesson, students will be able to:

Identify the hypotenuse and legs of a right triangle

Use the Pythagorean Theorem to find the length of a missing side in a right triangle

Apply the Pythagorean Theorem to solve real-life problems

Prerequisites

Before this lesson, students should be familiar with:

Basic understanding of triangles (including how to identify right triangles) and their properties, such as side lengths and angle measures

Basic algebra skills, including solving for unknown variables and simplifying equations

Familiarity with squaring and square roots

Colored pencils or markers

Pythagorean Theorem

Guided Notes

Key Vocabulary

Right triangle

Square Roots

Introduction

As a hook, ask students why the Pythagorean Theorem is important in real life, such as finding the dimensions of a baseball diamond. Use the guided notes to introduce the Pythagorean Theorem.

Walk through the key points of the topic of the guided notes to teach. Refer to the FAQs for a walk-through on this, as well as ideas on how to respond to common student questions.

For Page 1 of the guided notes, introduce the Pythagorean Theorem with the worked example "what do you notice."

For Page 2 of the guided notes, explain how to know which side is a, b, or c, and check for understanding. Based on student responses, reteach concepts that students need extra help with.

Have students practice using the Pythagorean Theorem with the Maze activity. Walk around to answer student questions.

Fast finishers can dive into the Doodle Math activity for extra practice. You can assign it as homework for the remainder of the class.

Real-Life Application

Bring the class back together, and introduce the concept of using the Pythagorean Theorem to determine the dimensions of a baseball diamond. Explain that the Pythagorean Theorem can be used to find the distance between any two points, even if they are not directly next to each other. In the case of a baseball diamond, the distance from home plate to first base, home plate to second base, and so on can be found by using the Pythagorean Theorem. Refer to the FAQ for more ideas on how to teach it!

Hands-on project

A fun, no-prep way for students to practice is my Pythagorean Spiral project . Students will use a square to draw successive triangles and create a spiral. They will then measure the spiral and solve for the length of the hypotenuse for every triangle in their Pythagorean spiral. At the end of the activity, students can turn their Pythagorean spiral into an art project.

Additional self-checking digital practice

If you’re looking for digital practice for the Pythagorean theorem, try my Pixel Art activities in Google Sheets. Every answer is automatically checked, and correct answers unlock parts of a mystery picture. It’s incredibly fun, and a powerful tool for differentiation.

There’s two version depending on the focus with your students:

Finding the hypotenuse and leg

. It’s available with fall , winter , Valentine’s Day , and St. Patrick’s Day themed images.

Challenge: Finding the distance between two points

. It’s available with Valentine’s Day and St. Patrick’s Day

themed images.

What is the Pythagorean theorem? Open

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In equation form, it can be written as a^2 + b^2 = c^2, where c is the length of the hypotenuse and a and b are the lengths of the other two sides.

How do you use the Pythagorean theorem to find the length of a missing side in a right triangle? Open

To use the Pythagorean theorem to find the length of a missing side in a right triangle, follow these steps:

Identify the two sides of the right triangle that are known.

Assign one of the sides as "a" and the other as "b."

Identify the hypotenuse of the right triangle

, which is the side opposite the right angle. Assign the hypotenuse as "c."

Plug the known values into the Pythagorean theorem

, which states that a^2 + b^2 = c^2. Solve for the unknown side by isolating it on one side of the equation and taking the square root of both sides.

For example, if the length of side a is 3 and the length of side b is 4, and you want to find the length of the hypotenuse (c), you would use the equation 3^2 + 4^2 = c^2. Simplifying, you get 9 + 16 = c^2, or 25 = c^2. Taking the square root of both sides gives you c = 5. Therefore, the length of the hypotenuse (c) is 5.

What is a hypotenuse? Open

A hypotenuse is the longest side of a right triangle and is opposite the right angle. It is the side that connects the two legs of the triangle.

What are the legs of a right triangle? Open

The legs of a right triangle are the two sides that form the right angle. They are usually labeled as 'a' and 'b'.

How do you identify a right triangle? Open

To identify a right triangle, you need to look for a triangle with one angle that measures 90 degrees, also known as a right angle. This means that one side of the triangle will be perpendicular to another side, forming the right angle.

What are some real-life applications of the Pythagorean theorem? Open

The Pythagorean theorem has a wide range of applications in real life. Some examples include:

Architecture:

Architects use the Pythagorean theorem to make sure that building corners are square, and to calculate the length of sloping roofs.

Navigation:

The Pythagorean theorem is used in navigation to determine distances between two points. This is particularly useful in aviation and marine navigation.

In sports, the Pythagorean theorem can be used to calculate the distance between bases on a baseball diamond, or to determine the length of a shot in basketball.

Surveyors use the Pythagorean theorem to measure distances between points on the earth's surface, and to calculate elevations.

In the classroom, students can apply the Pythagorean theorem to real-world problems, such as finding the distance between two points on a map or the height of a building. One particularly fun application is to use the Pythagorean theorem to find the dimensions of a baseball diamond, which involves using the theorem to calculate the distance between bases.

How do you find the dimensions of a baseball diamond using the Pythagorean theorem? Open

To find the dimensions of a baseball diamond using the Pythagorean theorem, you need to calculate the distance between the bases. Here's how:

Identify the two bases you want to calculate the distance between.

Draw a right triangle connecting the two bases and home plate, with the two bases forming the legs and the distance between them forming the hypotenuse.

Measure the distance between the bases and record it as one leg of the triangle.

Measure the distance from the starting base to home plate and record it as the other leg of the triangle.

Use the Pythagorean theorem (a^2 + b^2 = c^2) to solve for the hypotenuse, which represents the distance between the two bases.

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