Free Printable WorksheetMathGeometryMath CurriculumG-SRT.A.1-3

GEO.84 Similarity defined by dilations and 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.84 Similarity defined by dilations and rigid motions. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

GEO.84 Similarity defined by dilations and rigid motions - Primary standard selected for prompt fields in this prompt cell: CCSS G-SRT.A.1-3. Skill statement in this prompt cell: Select whether two figures are similar and identify the dilation and rigid-motion information that establishes similarity. Associated standards listed with this skill in the curriculum source: CCSS G-SRT.A.1-3; NY GEO G.G-SRT.A; MA G-SRT.A; FL MA.912.GR.2.8. 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.84 Similarity defined by dilations and rigid motions skill assessments:

Problem 1Difficulty: Mastery

Triangle PQR has vertices P(2,0), Q(2,4), and R(5,0). Triangle P'Q'R' has vertices P'(1,6), Q'(-7,6), and R'(1,12). Which sequence maps PQR to P'Q'R'?

ADilate centered at the origin by scale factor 2, rotate 90 degrees counterclockwise, then translate 1 unit right and 2 units up.

BDilate centered at the origin by scale factor 3, rotate 90 degrees counterclockwise, then translate 1 unit right and 2 units up.

CReflect across the y-axis, then translate 1 unit right and 2 units up.

DTranslate 1 unit right and 2 units up, then rotate 90 degrees counterclockwise.

Solution & Explanation:Dilation by 2 sends P, Q, R to (4,0), (4,8), and (10,0). A 90 degree counterclockwise rotation gives (0,4), (-8,4), and (0,10). Adding (1,2) gives (1,6), (-7,6), and (1,12).

Problem 2Difficulty: Mastery

A designer applies the rule (x,y) -> (1/4(x - 8) + 8, 1/4(y + 4) - 4) to every point of a figure. Which description is correct?

AIt is a dilation centered at (8,-4) with scale factor 1/4.

BIt is a dilation centered at the origin with scale factor 8.

CIt is a translation 8 units right and 4 units down.

DIt is not a similarity because fractions are used.

Solution & Explanation:The rule has the form center + k(point - center). The x-coordinate uses 8 + 1/4(x - 8), and the y-coordinate uses -4 + 1/4(y - (-4)), so the center is (8,-4) and k = 1/4.

Problem 3Difficulty: Mastery

Rectangle ABCD has vertices A(0,0), B(2,0), C(2,1), and D(0,1). Rectangle A'B'C'D' has vertices A'(1,1), B'(7,1), C'(7,4), and D'(1,4). Which proof of similarity is most precise?

ADilate ABCD centered at the origin by scale factor 3, then translate 1 unit right and 1 unit up.

BTranslate ABCD 1 unit right and 1 unit up only.

CRotate ABCD 90 degrees, then translate.

DThe rectangles are not similar because their coordinates are different.

Solution & Explanation:Dilation by 3 sends the rectangle to vertices (0,0), (6,0), (6,3), and (0,3). Translating by (1,1) gives exactly the listed image vertices.

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Frequently Asked Questions

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QHow do I download and print this GEO.84 Similarity defined by dilations and rigid motions 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-SRT.A.1-3 (Primary standard selected for prompt fields in this prompt cell: CCSS G-SRT.A.1-3. Skill statement in this prompt cell: Select whether two figures are similar and identify the dilation and rigid-motion information that establishes similarity. Associated standards listed with this skill in the curriculum source: CCSS G-SRT.A.1-3; NY GEO G.G-SRT.A; MA G-SRT.A; FL MA.912.GR.2.8. Use this prompt-provided wording as the supporting standard description for this workflow.).