Free Printable WorksheetMathGeometryMath CurriculumG-CO.D.12-13

GEO.67 Construct equilateral triangles and regular polygons Worksheet

Download our free printable Geometry Math worksheet on GEO.67 Construct equilateral triangles and regular polygons. Ideal for classroom practice, homeschool learning, independent homework, and standardized test preparation. Available in both print-ready PDF and editable DOCX formats.

Choose your preferred download format:

100% Free • No registration or login required • Instant file access

Download PDF Download DOCX

Prefer interactive practice with instant grading and explanations?Practice Construct equilateral triangles and regular polygons Online

Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Geometry Math worksheet provides structured practice on GEO.67 Construct equilateral triangles and regular polygons. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

GEO.67 Construct equilateral triangles and regular polygons - Primary standard selected for prompt fields in this prompt cell: CCSS G-CO.D.12-13. Skill statement in this prompt cell: Select the diagram or step sequence that correctly constructs an equilateral triangle, square, or regular hexagon, and identify the property that guarantees regularity. Associated standards listed with this skill in the curriculum source: CCSS G-CO.D.12-13; FL MA.912.GR.5.1-5.3; TEKS §111.41(c); MA G-CO.D.12-13. 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.67 Construct equilateral triangles and regular polygons skill assessments:

Problem 1Difficulty: Mastery

A teacher asks why classical constructions are exact rather than approximate. Which response is most precise for this skill?

AThe constructions use invariant distances from circles and perpendicular or equal-angle relationships, so regularity follows from geometric properties rather than visual guessing.

BThey are exact because every drawn figure on paper is automatically regular.

CThey are exact only after measuring every side with a ruler and rounding to the nearest unit.

DThey are exact because labels can be changed after the drawing is finished.

Solution & Explanation:Compass and straightedge methods create exact relationships such as congruent radii, perpendicular lines, and equal central angles. Those relationships prove regularity.

Problem 2Difficulty: Mastery

Which choice correctly matches each construction with the property that guarantees regularity?

AEquilateral triangle: three congruent sides; square: congruent sides and right angles; regular hexagon: equal radius-length chords and 60-degree central angles

BEquilateral triangle: one right angle; square: six central angles; regular hexagon: one pair of parallel sides

CEquilateral triangle: unequal radii; square: arbitrary slanted sides; regular hexagon: points chosen by sight

DEquilateral triangle: diameter endpoints; square: no angle conditions; regular hexagon: only one side measured

Solution & Explanation:Each listed property is the exact guarantee needed for regularity: equal sides for the regular triangle, equal sides plus right angles for the square, and equal chord spacing for the hexagon.

Problem 3Difficulty: Mastery

A construction sequence says: draw segment AB, draw circles centered at A and B with radius AB, choose intersection C, and connect AC and BC. Which extra step is not needed to prove triangle ABC is equilateral?

AMeasuring angle A with a protractor to check whether it looks like 60 degrees

BShowing C lies on the circle centered at A

CShowing C lies on the circle centered at B

DUsing the given segment AB as the compass radius

Solution & Explanation:The circle construction already guarantees AB = AC = BC. Measuring an angle is unnecessary and less exact than the construction proof.

Want more practice questions with step-by-step guidance?

Practice All Questions Online

Frequently Asked Questions

Common questions about printing, using, and solving this worksheet

QHow do I download and print this GEO.67 Construct equilateral triangles and regular polygons worksheet?

Click either the "Download PDF" or "Download DOCX" button at the top of the page. You can print the PDF directly from your browser or edit the DOCX file in Microsoft Word or Google Docs to tailor the questions to your students.

QIs this GEO.67 Construct equilateral triangles and regular polygons worksheet free for teachers and homeschoolers?

Yes! All learning materials, worksheets, and practice resources on Free K12 Practice are 100% free for teachers, students, parents, tutors, and homeschooling families for non-commercial educational use. No account or subscription is required.

QCan students practice GEO.67 Construct equilateral triangles and regular polygons online with instant feedback?

Yes! In addition to this printable worksheet, students can practice GEO.67 Construct equilateral triangles and regular polygons 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.D.12-13 (Primary standard selected for prompt fields in this prompt cell: CCSS G-CO.D.12-13. Skill statement in this prompt cell: Select the diagram or step sequence that correctly constructs an equilateral triangle, square, or regular hexagon, and identify the property that guarantees regularity. Associated standards listed with this skill in the curriculum source: CCSS G-CO.D.12-13; FL MA.912.GR.5.1-5.3; TEKS §111.41(c); MA G-CO.D.12-13. Use this prompt-provided wording as the supporting standard description for this workflow.).