Free Printable WorksheetMathGeometryMath CurriculumG-SRT.B.4-5

GEO.91 Right triangle geometric mean relationships Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Geometry Math worksheet provides structured practice on GEO.91 Right triangle geometric mean relationships. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

GEO.91 Right triangle geometric mean relationships - Primary standard selected for prompt fields in this prompt cell: CCSS G-SRT.B.4-5. Skill statement in this prompt cell: Select the correct geometric-mean relationship in a right triangle and compute the missing length. Associated standards listed with this skill in the curriculum source: CCSS G-SRT.B.4-5; NY GEO G.G-SRT.B; MA G-SRT.B; FL MA.912.GR.1.2, 1.6. 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.91 Right triangle geometric mean relationships skill assessments:

Problem 1Difficulty: Mastery
An altitude divides a 150-unit hypotenuse into segments 30 units and 120 units. Which complete set of missing lengths is correct?
Aaltitude 60 units, legs 30 sqrt(5) units and 60 sqrt(5) units
Baltitude 90 units, legs 30 sqrt(5) units and 60 sqrt(5) units
Caltitude 60 units, legs 30 units and 120 units
Daltitude 30 sqrt(5) units, legs 60 units and 120 units
Solution & Explanation:The altitude is sqrt(30*120) = sqrt(3600) = 60. The legs are sqrt(150*30) = 30 sqrt(5) and sqrt(150*120) = 60 sqrt(5).
Problem 2Difficulty: Mastery
A right triangle has hypotenuse 125 units and altitude to the hypotenuse 50 units. The hypotenuse segments are 25 and 100. What is the shorter leg?
A25 sqrt(5) units
B50 units
C50 sqrt(5) units
D100 units
Solution & Explanation:The shorter leg is adjacent to the 25-unit segment. Use x2 = 125*25 = 3125, so x = 25 sqrt(5).
Problem 3Difficulty: Mastery
The hypotenuse is 80 units, and the altitude to the hypotenuse is 20 sqrt(3) units. The segments are 20 and 60. What is the shorter leg?
A20 sqrt(3) units
B40 units
C40 sqrt(3) units
D60 units
Solution & Explanation:The shorter leg is adjacent to the shorter segment, 20. Use x2 = 80*20 = 1600, so x = 40 units.

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Frequently Asked Questions

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QIs this GEO.91 Right triangle geometric mean relationships worksheet free for teachers and homeschoolers?

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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.B.4-5 (Primary standard selected for prompt fields in this prompt cell: CCSS G-SRT.B.4-5. Skill statement in this prompt cell: Select the correct geometric-mean relationship in a right triangle and compute the missing length. Associated standards listed with this skill in the curriculum source: CCSS G-SRT.B.4-5; NY GEO G.G-SRT.B; MA G-SRT.B; FL MA.912.GR.1.2, 1.6. Use this prompt-provided wording as the supporting standard description for this workflow.).

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