Free Printable WorksheetMathGeometryMath CurriculumG-SRT.C.6-8

GEO.108 Choose and use a special right triangle ratio Worksheet

Download our free printable Geometry Math worksheet on GEO.108 Choose and use a special right triangle ratio. 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

Prefer interactive practice with instant grading and explanations?Practice Choose and use a special right triangle ratio Online

Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Geometry Math worksheet provides structured practice on GEO.108 Choose and use a special right triangle ratio. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

GEO.108 Choose and use a special right triangle ratio - Primary standard selected for prompt fields in this prompt cell: CCSS G-SRT.C.6-8. Skill statement in this prompt cell: Select the special right triangle type and choose the correct missing length using its ratio. Associated standards listed with this skill in the curriculum source: CCSS G-SRT.C.6-8; VA G.TR.4; FL MA.912.T.1.*; TEKS §111.41(c). Use this prompt-provided wording as the supporting standard description for this workflow.

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

Geometry

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 GEO.108 Choose and use a special right triangle ratio skill assessments:

Problem 1Difficulty: Mastery
A logo uses two right triangles that share a hypotenuse of 30 units. One triangle is 45-45-90 and the other is 30-60-90. Which pair of missing side lengths is correct?
A45-45-90 leg 15 sqrt(2); 30-60-90 legs 15 and 15 sqrt(3)
B45-45-90 leg 15; 30-60-90 legs 15 sqrt(2) and 15 sqrt(3)
C45-45-90 leg 30 sqrt(2); 30-60-90 legs 30 and 30 sqrt(3)
D45-45-90 leg 15 sqrt(3); 30-60-90 legs 15 and 15 sqrt(2)
Solution & Explanation:For the 45-45-90 triangle, each leg is 30/sqrt(2) = 15 sqrt(2). For the 30-60-90 triangle, the shorter leg is 15 and the longer leg is 15 sqrt(3).
Problem 2Difficulty: Mastery
A 30-60-90 triangle has perimeter 12 + 4 sqrt(3) units. A 45-45-90 triangle is built with the same length as the shorter leg of the 30-60-90 triangle. What is the hypotenuse of the 45-45-90 triangle?
A4 units
B4 sqrt(2) units
C8 units
D8 sqrt(2) units
Solution & Explanation:A 30-60-90 perimeter is 3x + x sqrt(3). Matching 12 + 4 sqrt(3) gives x = 4. A 45-45-90 triangle with leg 4 has hypotenuse 4 sqrt(2).
Problem 3Difficulty: Mastery
A right triangle has side lengths 11, 11, and 11 sqrt(2) units. Which special triangle type and angle measures match these lengths?
A45-45-90 with acute angles 45 degrees and 45 degrees
B30-60-90 with acute angles 30 degrees and 60 degrees
C45-45-90 with acute angles 30 degrees and 60 degrees
D30-60-90 with acute angles 45 degrees and 45 degrees
Solution & Explanation:The two equal sides are the legs and the hypotenuse is leg times sqrt(2). That is the 45-45-90 ratio, so the acute angles are 45 degrees and 45 degrees.

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 GEO.108 Choose and use a special right triangle ratio 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 GEO.108 Choose and use a special right triangle ratio 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 GEO.108 Choose and use a special right triangle ratio online with instant feedback?

Yes! In addition to this printable worksheet, students can practice GEO.108 Choose and use a special right triangle ratio 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 Geometry Math students. It aligns with educational standard G-SRT.C.6-8 (Primary standard selected for prompt fields in this prompt cell: CCSS G-SRT.C.6-8. Skill statement in this prompt cell: Select the special right triangle type and choose the correct missing length using its ratio. Associated standards listed with this skill in the curriculum source: CCSS G-SRT.C.6-8; VA G.TR.4; FL MA.912.T.1.*; TEKS §111.41(c). Use this prompt-provided wording as the supporting standard description for this workflow.).

Related Geometry Math Resources

Continue learning with complementary skill worksheets and online practice