Free Printable WorksheetMathGrade 8Math Curriculum8.G.A.2

8.117 Understanding Congruence Through Rigid Motions Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Grade 8 Math worksheet provides structured practice on 8.117 Understanding Congruence Through Rigid Motions. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

8.117 Understanding Congruence Through Rigid Motions - Which conclusion about congruence is correct based on the rigid motions that map one figure to the other? (CCSS 8.G.A.2; CA 8.G.A.2; MA 8.G.A.2)

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

Grade 8

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 8.117 Understanding Congruence Through Rigid Motions skill assessments:

Problem 1Difficulty: Hard

Pentagon MNOPQ has vertices M(1, -5), N(5, 1), O(3, 2), P(4, 6), and Q(-2, 3). Pentagon M'N'O'P'Q' has vertices M'(5, -6), N'(7, -1), O'(5, 0), P'(6, 4), and Q'(0, 1). Which explanation best shows that the two figures are not congruent?

AThe figures are not congruent because they do not start in the same quadrant.

BThe figures are not congruent because every reflection changes the size of a figure.

CThe figures are not congruent because they are labeled with different letters.

DOne vertex does not follow the same translation as the others, so the distances between corresponding points are not preserved.

Solution & Explanation:One vertex does not follow the same translation as the others, so the distances between corresponding points are not preserved. Congruent figures must be related by rigid motions that preserve all distances.

Problem 2Difficulty: Hard

Pentagon GHIJK has vertices G(-4, -4), H(-2, 0), I(4, 5), J(-2, 4), and K(-6, 5). Pentagon G'H'I'J'K' has vertices G'(-8, -4), H'(-4, 0), I'(8, 5), J'(-4, 4), and K'(-12, 5). Which explanation best shows that the two figures are not congruent?

AThe x-coordinates are scaled by 2, so the side lengths do not all stay the same.

BThe figures are not congruent because they do not start in the same quadrant.

CThe figures are not congruent because they are labeled with different letters.

DThe figures are not congruent because every reflection changes the size of a figure.

Solution & Explanation:The x-coordinates are scaled by 2, so the side lengths do not all stay the same. Congruent figures must be related by rigid motions that preserve all distances.

Problem 3Difficulty: Hard

Pentagon BCDEF has vertices B(-6, -4), C(-2, -6), D(5, 1), E(3, 6), and F(0, 0). Pentagon B'C'D'E'F' has vertices B'(-12, -8), C'(-4, -12), D'(10, 2), E'(6, 12), and F'(0, 0). Which explanation best shows that the two figures are not congruent?

AThe figures are not congruent because translations always reverse orientation.

BThe figures are not congruent because only triangles can be congruent.

CThe figures are not congruent because they are labeled with different letters.

DThe corresponding distances are multiplied by 2, so the mapping is a dilation, not a rigid motion.

Solution & Explanation:The corresponding distances are multiplied by 2, so the mapping is a dilation, not a rigid motion. Congruent figures must be related by rigid motions that preserve all distances.

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Grade 8 Math students. It aligns with educational standard 8.G.A.2 (Primary standard selected for prompt fields: CCSS 8.G.A.2. Skill statement: Which conclusion about congruence is correct based on the rigid motions that map one figure to the other? Associated standards listed with this skill: CCSS 8.G.A.2; CA 8.G.A.2; MA 8.G.A.2. Use this embedded wording as the best available supporting standard description for this workflow.).