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

GEO.77 Determine whether two figures are congruent from a transformation Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Geometry Math worksheet provides structured practice on GEO.77 Determine whether two figures are congruent from a transformation. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

GEO.77 Determine whether two figures are congruent from a transformation - Primary standard selected for prompt fields in this prompt cell: CCSS G-CO.B.6-8. Skill statement in this prompt cell: Select whether the figures are congruent and choose the correct matching of corresponding vertices, sides, or angles. 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.77 Determine whether two figures are congruent from a transformation skill assessments:

Problem 1Difficulty: Mastery

Triangle ABC has A(1, 4), B(3, 0), and C(-2, 2). It is reflected over y = x, rotated 180 degrees about the origin, and translated by (2, -3). The final image points are D(2, -6), E(0, -1), and F(-2, -4). Which conclusion and matching are correct?

AThe triangles are congruent; A to F, B to D, and C to E.

BThe triangles are congruent; A to D, B to E, and C to F.

CThe triangles are not congruent because three transformations were used.

DThe triangles are not congruent because reflection over y = x changes size.

Solution & Explanation:Each step is a rigid motion. The coordinate sequence maps A to F, B to D, and C to E, so the triangles are congruent with that correspondence.

Problem 2Difficulty: Mastery

Quadrilateral ABCD and quadrilateral PQRS have the same side lengths in order, and the proposed correspondence is A to P, B to Q, C to R, and D to S. However, diagonal AC is 10 while diagonal PR is 12. Which conclusion is correct?

AThe quadrilaterals are congruent because side lengths in order are enough for any quadrilateral.

BThe proposed correspondence cannot come from a rigid transformation because a diagonal distance is not preserved.

CThe quadrilaterals are congruent because diagonals do not matter in transformations.

DThe proposed correspondence is correct only if the figures are reflected.

Solution & Explanation:Rigid transformations preserve the distance between every pair of corresponding points, including diagonal endpoints. If AC and PR differ, the proposed correspondence is impossible.

Problem 3Difficulty: Mastery

A 180-degree rotation of hexagon ABCDEF maps A to D, B to E, C to F, D to A, E to B, and F to C. Which side corresponds to side EF?

Aside AB

Bside BC

Cside CD

Dside DA

Solution & Explanation:The endpoints E and F map to B and C. Therefore side EF corresponds to side BC.

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Frequently Asked Questions

Common questions about printing, using, and solving this worksheet

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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-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 the figures are congruent and choose the correct matching of corresponding vertices, sides, or angles. 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.).