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"Lines, Angles, and Triangles: Lesson 7 - The Pythagorean Relationship." Teachers' Domain. 18 Apr. 2011. Web. 24 May. 2013. <http://www.teachersdomain.org/resource/geopd.math.geo.modblessseven/>.

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On the GED^® Mathematics Test, students are likely to encounter problems that involve right triangle relationships.

Students will need to solve for the value of the hypotenuse of a right triangle, using the Pythagorean relationship.
They will also need to use the Pythagorean relationship to find a missing side by solving for an unknown.

This lesson introduces the Pythagorean relationship. To answer right triangle questions successfully, GED students need to recognize a right triangle when it is embedded in a setting. They need to use the formulas page that is part of the GED Mathematics Test, access the Pythagorean relationship, and solve for the hypotenuse or an unknown side.

Module B: Lesson 7 Credit

2 Solve for the Hypotenuse

Watch the video for a demonstration of using the Pythagorean relationship to solve a problem.

B7 Page 2 Triangle 2

B7 Page 2 Triangle 1

B7 Page 2 Triangle 3

Triangles: The Pythagorean Relationship

Video: 1m 49s

In any right triangle, the side opposite the right angle is the hypotenuse. It is the longest side. The other two sides are the legs.

The hypotenuse and the legs are related by the Pythagorean relationship. Below is the formula

a² + b² = c²

The legs are a and b.

The hypotenuse is c.

The Pythagorean formula is included on the GED formulas page, which will be provided to students when they take the GED Mathematics Test

B7 Page 2 Image 1

Question The diagram at left shows the design for the 4-foot end of a theater platform. The top and legs of the platform form right angles.

What is the length of the diagonal brace?

Step 1 Identify the legs and hypotenuse of the right triangle.

The legs of the right triangle are 4 ft and 3 ft.

The brace is opposite the right angle. It is the hypotenuse.

Step 2 Use the Pythagorean formula and substitute. Remember, the hypotenuse is always the letter variable c.

a² + b² = c² ← write the formula

16 + 9 = c² ← square 4 and square 3

Step 3 Solve to find c, the length of the brace.

4² + 3² = c²

16 + 9 = c² ← square 4 and square 3

25 = c² ← add to simplify

√25 = c ← take the square root of both sides

5 = c

Answer 5 feet

3 Find a Missing Side

In some right-triangle problems, you are given the hypotenuse and one leg. You are asked to find the other leg. This leg is unknown or “missing.”

Use the Pythagorean relationship to find a missing leg.

a² + b² = c²

The legs are a and b.

The hypotenuse is c.

B7 Page 3 Image 1

Question A cross-section of a small wood wedge looks like the triangle below.

Find b, the length of the wedge.

Step 1 Identify the legs and hypotenuse of the right triangle.

left leg = 5 cm; hypotenuse = 13 cm

The bottom leg is b. It is the unknown length.

Step 2 Use the Pythagorean formula and substitute. Remember, the hypotenuse is always the letter variable c.

a² + b² = c² ← write the formula

5² + b² = 13² ← substitute 5 for a and 13 for c

Step 3 Solve to find leg b, the length of the wedge.

5² + b² = 13²

25 + b² = 169 ← square 5 and square 13

25 – 25 + b² = 169 – 25 ← subtract 25 from both sides

b² = 144 ← b² is isolated

b = √144 ← take the square root of both sides

b = 12

Answer 12 cm.

4 Sample GED Questions

Directions: There are two questions on this page. Each will appear in the blue rectangle below. Click on Question 1 to see the first question, and then select your answer. Click on Question 2 to see the second question, and select your answer. As you solve these problems, also respond to the questions related to building students’ skills.

How could you help students identify the legs and the hypotenuse of the right triangle and relate the description of the pole, brace, and building to the diagram?

Click here for more teaching ideas.

5 Skill Review

Lines, Angles, and Triangles: The Pythagorean Relationship Skill Review

Document

Printable Resource

In this lesson you have learned about the Pythagorean relationship. This review consists of key terms and concepts with which you will need to be familiar. Click the view button on the left to access a review sheet.

Below you will also see a Classroom Connection with suggestions for linking this geometry content with your instruction.

Module B Lesson 7: Class Connection

Return to the GED Online Professional Development Course.

Credits

Screen 1:

Screen 2:

Triangles: The Pythagorean Relationship (Video)
Producer/Director: Vince Spoelker
Editor: Jim Piston

Screen 3:

Screen 4:

Module B Lesson 7: GED Questions (Interactive)
Flash Programming: Dave Hamon

Screen 5:

1 2 3 4 5

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Lines, Angles, and Triangles: Lesson 7 - The Pythagorean Relationship

Activity for Grades 9-12

Teachers' Domain, Lines, Angles, and Triangles: Lesson 7 - The Pythagorean Relationship, published April 18, 2011, retrieved on ,
http://www.teachersdomain.org/resource/geopd.math.geo.modblessseven/

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The Pythagorean Relationship is the seventh of eight self-paced lessons in the “Lines, Angles, and Triangles” section of KET’s GED^® Geometry Professional Development Online Course. This lesson introduces the Pythagorean Relationship, identifies the legs and the hypotenuse of a right triangle, and shows how to solve for a missing side of a triangle.

KET’s GED Geometry Professional Development Online Course is designed to help you review and build your skills and knowledge of geometry concepts and to help you to gain confidence in preparing your learners for a substantial portion of the GED Mathematics Test. Click on the view button on the left to begin Lesson 7.

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