Free Printable WorksheetMathGeometryMath CurriculumG-CO.B.6-8

GEO.55 Congruence defined by rigid motions Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Geometry Math worksheet provides structured practice on GEO.55 Congruence defined by rigid motions. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

GEO.55 Congruence defined by rigid motions - Primary standard selected for prompt fields in this prompt cell: CCSS G-CO.B.6-8. Skill statement in this prompt cell: Select whether two figures are congruent and choose the rigid motion or sequence of rigid motions that maps one figure onto the other. Associated standards listed with this skill in the curriculum source: CCSS G-CO.B.6-8; NY GEO G.G-CO.B; FL MA.912.GR.2.6; 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.55 Congruence defined by rigid motions skill assessments:

Problem 1Difficulty: Mastery

Quadrilateral ABCD has vertices A(-2, 1), B(1, 1), C(2, 4), and D(-1, 5). Quadrilateral A'B'C'D' has vertices A'(4, -3), B'(4, 0), C'(1, 1), and D'(0, -2). Which sequence maps ABCD onto A'B'C'D'?

ARotate 90 degrees clockwise about the origin, then translate 5 units right and 1 unit down

BReflect over the x-axis, then translate 5 units right

CTranslate 5 units right and 1 unit down, then rotate 90 degrees counterclockwise

DRotate 90 degrees counterclockwise about the origin, then translate 5 units right and 1 unit down

Solution & Explanation:A 90-degree counterclockwise rotation sends the vertices to (-1,-2), (-1,1), (-4,2), and (-5,-1). Translating by (5,-1) gives (4,-3), (4,0), (1,1), and (0,-2).

Problem 2Difficulty: Mastery

Triangle ABC has vertices A(5, 4), B(5, 7), and C(8, 4). Triangle A'B'C' has vertices A'(-1, 2), B'(-1, -1), and C'(-4, 2). Which rigid motion maps ABC onto A'B'C'?

ARotate 180 degrees about the origin

BReflect over the x-axis, then translate 6 units left

CRotate 180 degrees about the point (2, 3)

DTranslate 6 units left and 2 units down

Solution & Explanation:A 180-degree rotation about (h, k) sends (x, y) to (2h - x, 2k - y). With center (2,3), the rule is (x, y)->(4 - x, 6 - y), which maps all three vertices to the image.

Problem 3Difficulty: Mastery

Triangle ABC has vertices A(0, 0), B(3, 0), and C(0, 4). Which labeled triangle A'B'C' could be the image of ABC under a rigid motion with A mapping to A', B mapping to B', and C mapping to C'?

AA'(0, 0), B'(6, 0), C'(0, 8)

BA'(2, 1), B'(5, 1), C'(2, 5)

CA'(1, 1), B'(4, 1), C'(1, 6)

DA'(0, 0), B'(0, 4), C'(3, 0)

Solution & Explanation:With the labels fixed, AB must stay 3 units and AC must stay 4 units. Only A'(2,1), B'(5,1), and C'(2,5) preserve those corresponding distances.

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Frequently Asked Questions

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QHow do I download and print this GEO.55 Congruence defined by rigid motions worksheet?

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QIs this GEO.55 Congruence defined by rigid motions worksheet free for teachers and homeschoolers?

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Yes! In addition to this printable worksheet, students can practice GEO.55 Congruence defined by rigid motions 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-CO.B.6-8 (Primary standard selected for prompt fields in this prompt cell: CCSS G-CO.B.6-8. Skill statement in this prompt cell: Select whether two figures are congruent and choose the rigid motion or sequence of rigid motions that maps one figure onto the other. Associated standards listed with this skill in the curriculum source: CCSS G-CO.B.6-8; NY GEO G.G-CO.B; FL MA.912.GR.2.6; TEKS §111.41(c). Use this prompt-provided wording as the supporting standard description for this workflow.).