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

GEO.94 Special right triangles Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Geometry Math worksheet provides structured practice on GEO.94 Special right triangles. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

GEO.94 Special right triangles - Primary standard selected for prompt fields in this prompt cell: CCSS G-SRT.C.6-8. Skill statement in this prompt cell: Identify the special right triangle type and select the correct missing side length using known ratios. 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.94 Special right triangles skill assessments:

Problem 1Difficulty: Mastery
A student divides the hypotenuse 14 sqrt(2) by 2 and claims a leg of a 45-45-90 triangle is 7 sqrt(2). Which option correctly identifies the triangle type and leg x?
A30-60-90; x = 7 sqrt(2) units
B45-45-90; x = 14 sqrt(2) units
C45-45-90; x = 14 units
D30-60-90; x = 14 sqrt(3) units
Solution & Explanation:In a 45-45-90 triangle, hypotenuse = leg times sqrt(2), not twice the leg. Since 14 sqrt(2) = x sqrt(2), the leg is x = 14 units.
Problem 2Difficulty: Mastery
A 30-60-90 triangle has longer leg equal to the diagonal of a square with side length 6 units. The hypotenuse is x. Which special right triangle type gives x, and what is x?
A45-45-90; x = 6 sqrt(2) units
B30-60-90; x = 4 sqrt(6) units
C30-60-90; x = 12 units
D45-45-90; x = 6 units
Solution & Explanation:The square diagonal is 6 sqrt(2). In the 30-60-90 triangle, a sqrt(3) = 6 sqrt(2), so a = 2 sqrt(6). The hypotenuse is 2a = 4 sqrt(6) units.
Problem 3Difficulty: Mastery
A 45-45-90 triangle has one leg equal to the shorter leg of a 30-60-90 triangle whose hypotenuse is 26 centimeters. The 45-45-90 hypotenuse is x. Which special right triangle type gives x, and what is x?
A30-60-90; x = 26 centimeters
B45-45-90; x = 13 centimeters
C30-60-90; x = 13 sqrt(3) centimeters
D45-45-90; x = 13 sqrt(2) centimeters
Solution & Explanation:The shorter leg of the 30-60-90 triangle is half of 26, or 13. That becomes a leg of the 45-45-90 triangle, so its hypotenuse is 13 sqrt(2) centimeters.

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Frequently Asked Questions

Common questions about printing, using, and solving this worksheet

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QIs this GEO.94 Special right triangles worksheet free for teachers and homeschoolers?

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Yes! In addition to this printable worksheet, students can practice GEO.94 Special right triangles 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: Identify the special right triangle type and select the correct missing side length using known ratios. 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.).

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