Free Printable WorksheetMathGrade 8Math Curriculum8.G.B.6

8.131 Using the Converse of the Pythagorean Theorem Worksheet

Download our free printable Grade 8 Math worksheet on 8.131 Using the Converse of the Pythagorean Theorem. Ideal for classroom practice, homeschool learning, independent homework, and standardized test preparation. Available in both print-ready PDF and editable DOCX formats.

Choose your preferred download format:

100% Free • No registration or login required • Instant file access

Download PDF Download DOCX

Prefer interactive practice with instant grading and explanations?Practice Using the Converse of the Pythagorean Theorem Online

Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Grade 8 Math worksheet provides structured practice on 8.131 Using the Converse of the Pythagorean Theorem. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

8.131 Using the Converse of the Pythagorean Theorem - Based on the side lengths given, which conclusion about whether the triangle is a right triangle is correct? (CCSS 8.G.B.6; CA 8.G.B.6; MA 8.G.B.6)

Whether you are an educator preparing classroom handouts, a tutor reinforcing weekly topics, or a parent supporting homeschool learning, this printable resource gives students the deliberate practice required to achieve subject fluency and master state standards.

Grade

Grade 8

Subject

Math

Domain

Math Curriculum

Formats

PDF & DOCX

Sample Practice Problems

Preview the types of problems and questions covered in this worksheet

Below are sample questions representative of the exercises included on this worksheet and related 8.131 Using the Converse of the Pythagorean Theorem skill assessments:

Problem 1Difficulty: Hard

A student checks side lengths 86 in, 53 in, and 101 in and says, 'The triangle is right because all three side lengths are different.' Which option is correct?

AAria is correct because 53 + 86 > 101.

BAria is not correct. Different side lengths do not prove a right triangle. You still need to compare 53² + 86² with 101².

CAria is correct because the longest side does not matter.

DAria is not correct because you should subtract the side lengths.

Solution & Explanation:Use the longest side as c. 53² + 86² = 10205, but 101² = 10201. Since they are not equal, the triangle is not right.

Problem 2Difficulty: Hard

Leo examines a triangle with side lengths 174 cm, 155 cm, and 79 cm and says, 'Because 79² + 155² is not equal to 174², the triangle is not right.' What is the best response?

ALeo is not correct because the triangle does not have equal side lengths.

BLeo is not correct because the shortest side should be squared alone.

CLeo is correct. Using the two shorter sides and the longest side is the correct way to apply the converse.

DLeo is correct because the side lengths add to an even number.

Solution & Explanation:Use the longest side as c. 79² + 155² = 30266, but 174² = 30276. Since they are not equal, the triangle is not right.

Problem 3Difficulty: Hard

After measuring side lengths 143 m, 145 m, and 24 m, Nora writes, 'Because 24² + 143² = 145², the triangle is right.' Which answer correctly evaluates the claim?

ANora is not correct because the side lengths should be added, not squared.

BNora is correct because the converse compares the squares of the two shorter sides with the square of the longest side.

CNora is not correct because a right triangle must have equal sides.

DThe claim cannot be checked from side lengths.

Solution & Explanation:Use the longest side as c. 24² + 143² = 21025, and 145² = 21025. Since they are equal, the triangle is right.

Want more practice questions with step-by-step guidance?

Practice All Questions Online

Frequently Asked Questions

Common questions about printing, using, and solving this worksheet

QHow do I download and print this 8.131 Using the Converse of the Pythagorean Theorem worksheet?

Click either the "Download PDF" or "Download DOCX" button at the top of the page. You can print the PDF directly from your browser or edit the DOCX file in Microsoft Word or Google Docs to tailor the questions to your students.

QIs this 8.131 Using the Converse of the Pythagorean Theorem worksheet free for teachers and homeschoolers?

Yes! All learning materials, worksheets, and practice resources on Free K12 Practice are 100% free for teachers, students, parents, tutors, and homeschooling families for non-commercial educational use. No account or subscription is required.

QCan students practice 8.131 Using the Converse of the Pythagorean Theorem online with instant feedback?

Yes! In addition to this printable worksheet, students can practice 8.131 Using the Converse of the Pythagorean Theorem interactively on our platform with automated grading, instant score tracking, and detailed step-by-step solutions.

QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Grade 8 Math students. It aligns with educational standard 8.G.B.6 (Primary standard selected for prompt fields: CCSS 8.G.B.6. Skill statement: Based on the side lengths given, which conclusion about whether the triangle is a right triangle is correct? Associated standards listed with this skill: CCSS 8.G.B.6; CA 8.G.B.6; MA 8.G.B.6. Use this embedded wording as the best available supporting standard description for this workflow.).