Free Printable WorksheetMathGeometryMath CurriculumG-C.A.1

GEO.114 Prove and use that all circles are similar Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Geometry Math worksheet provides structured practice on GEO.114 Prove and use that all circles are similar. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

GEO.114 Prove and use that all circles are similar - Primary standard selected for prompt fields in this prompt cell: CCSS G-C.A.1. Skill statement in this prompt cell: Select the transformation-based explanation that shows all circles are similar and identify how measures change under scaling. Associated standards listed with this skill in the curriculum source: CCSS G-C.A.1; NY GEO G.G-C.A.1; MA G-C.A.1. 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.114 Prove and use that all circles are similar skill assessments:

Problem 1Difficulty: Mastery

Circle A has center (-3, 2) and radius 4. Circle B has center (5, -1) and radius 14. Which capstone explanation is correct?

ATranslate by (8, -3), dilate by 7/2 about the new center, multiply linear measures by 7/2, multiply areas by 49/4, and keep angle measures unchanged.

BTranslate by (-8, 3), dilate by 7/2, multiply linear measures by 49/4, and keep area unchanged.

CTranslate by (8, -3), dilate by 4/14, multiply areas by 7/2, and double all angles.

DTranslate by (5, -1), then add 10 units to each radius and multiply angles by 7/2.

Solution & Explanation:The center translation is (5 - (-3), -1 - 2) = (8, -3). The scale factor is 14/4 = 7/2. Linear measures scale by 7/2, areas by (7/2)² = 49/4, and angles are unchanged.

Problem 2Difficulty: Mastery

A target circle has radius 2.5 times the source circle's radius. Which complete statement about corresponding measures is correct?

ADiameter, circumference, and arc length multiply by 2.5; area and sector area multiply by 6.25; central angles stay the same.

BDiameter, circumference, and arc length multiply by 6.25; area and sector area multiply by 2.5; central angles stay the same.

CAll measures, including central angles, multiply by 2.5.

DOnly radius changes; all other circle measures are unchanged.

Solution & Explanation:The scale factor is 2.5. Linear measures multiply by 2.5, area measures multiply by 2.5² = 6.25, and angle measures are preserved.

Problem 3Difficulty: Mastery

Which statement correctly distinguishes similarity from congruence for circles?

AAll circles are similar, but only circles with equal radii are congruent.

BAll circles are congruent, but only circles with equal centers are similar.

CCircles with different radii are neither similar nor congruent.

DTwo circles are congruent only when their areas have ratio k².

Solution & Explanation:A dilation can change radius to prove similarity. Congruence requires rigid motions only, so the radii must be equal.

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Frequently Asked Questions

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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-C.A.1 (Primary standard selected for prompt fields in this prompt cell: CCSS G-C.A.1. Skill statement in this prompt cell: Select the transformation-based explanation that shows all circles are similar and identify how measures change under scaling. Associated standards listed with this skill in the curriculum source: CCSS G-C.A.1; NY GEO G.G-C.A.1; MA G-C.A.1. Use this prompt-provided wording as the supporting standard description for this workflow.).