Free Printable WorksheetMathGeometryMath CurriculumGEO.18

GEO.18 Use counterexamples to test conjectures Worksheet

Download our free printable Geometry Math worksheet on GEO.18 Use counterexamples to test conjectures. 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 Use counterexamples to test conjectures Online

Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Geometry Math worksheet provides structured practice on GEO.18 Use counterexamples to test conjectures. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

GEO.18 Use counterexamples to test conjectures - High school geometry skill focused on counterexamples in geometry.

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.18 Use counterexamples to test conjectures skill assessments:

Problem 1Difficulty: Mastery

Conjecture: If one diagonal of a quadrilateral is the perpendicular bisector of the other diagonal, then the quadrilateral must be a rhombus. Which option is a counterexample?

AA square (each diagonal is a perpendicular bisector of the other)

BA rhombus (diagonals are perpendicular bisectors)

CA rectangle that is not a square (diagonals bisect but are not perpendicular)

DQuadrilateral with vertices A(-2,0), B(0,3), C(2,0), D(0,-1) where BD is perpendicular to AC and passes through the midpoint of AC

Solution & Explanation:If one diagonal is the perpendicular bisector of the other, the quadrilateral is a kite, not necessarily a rhombus. In option D, BD is a perpendicular bisector of AC, but the side lengths are √13, √13, √5, √5, so not all four sides are equal. Therefore it is not a rhombus, making D a counterexample.

Problem 2Difficulty: Mastery

Conjecture: If a quadrilateral has congruent diagonals, then its vertices must lie on a single circle (the quadrilateral is cyclic). Which option is a counterexample?

AA rectangle (diagonals congruent and it is cyclic)

BAn isosceles trapezoid (diagonals congruent and it is cyclic)

CQuadrilateral with vertices A(-5,0), B(0,7), C(5,0), D(0,-3) where AC = 10 and BD = 10

DA square (diagonals congruent and it is cyclic)

Solution & Explanation:Congruent diagonals do not guarantee a cyclic quadrilateral. In option C, the diagonals are both 10, but opposite angles are not supplementary (for example, ∠B ≈ 71° and ∠D ≈ 118°, which sum to about 189°), so the points are not concyclic. Thus C is a counterexample.

Problem 3Difficulty: Mastery

Conjecture: If two triangles have the same inradius, then the triangles are congruent. Which option is a counterexample?

ATwo congruent triangles (same inradius and same shape)

BA 3–4–5 right triangle (inradius 1) and an equilateral triangle with side length 2√3 (inradius 1)

CA 3–4–5 right triangle (inradius 1) and a 6–8–10 right triangle (inradius 2)

DTwo equilateral triangles with side lengths 2√3 and 4√3 (inradii 1 and 2)

Solution & Explanation:Different triangles can share the same inradius. In option B, both triangles have inradius 1, but a 3–4–5 triangle is not congruent to an equilateral triangle. So B is a counterexample.

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.18 Use counterexamples to test conjectures 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.18 Use counterexamples to test conjectures 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.18 Use counterexamples to test conjectures online with instant feedback?

Yes! In addition to this printable worksheet, students can practice GEO.18 Use counterexamples to test conjectures 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 GEO.18 (High school geometry skill focused on counterexamples in geometry.).