Free Printable WorksheetMathGeometryMath CurriculumG-GPE.B.6

GEO.140 Coordinate proofs of geometric theorems Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Geometry Math worksheet provides structured practice on GEO.140 Coordinate proofs of geometric theorems. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

GEO.140 Coordinate proofs of geometric theorems - Primary standard selected for prompt fields in this prompt cell: CCSS G-GPE.B.6. Skill statement in this prompt cell: Select the slope or distance relationship that proves a geometric claim in the coordinate plane. Associated standards listed with this skill in the curriculum source: CCSS G-GPE.B.6; MA G-GPE.B.6; NY GEO G.G-GPE.B.6. 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.140 Coordinate proofs of geometric theorems skill assessments:

Problem 1Difficulty: Mastery
Quadrilateral ABCD has vertices A(1, -3), B(4, 3), C(10, 0), D(7, -6). Which relationship proves ABCD is a parallelogram with perpendicular diagonals?
AAB2 = BC2 = CD2 = DA2 only
Bm_AC = m_BD
Cm_AB and m_BC are negative reciprocals
Dm_AB = m_CD = 2, m_BC = m_AD = -1/2, and m_AC = 1/3, m_BD = -3
Solution & Explanation:Equal slopes for both pairs of opposite sides prove a parallelogram. The diagonals have slopes 1/3 and -3, which are negative reciprocals, so the diagonals are perpendicular.
Problem 2Difficulty: Mastery
Quadrilateral ABCD has vertices A(-5, -2), B(1, 2), C(3, 5), D(0, 3). Which relationship proves that one pair of opposite sides is parallel but the other pair is not?
AAB2 = CD2 = 52
Bm_AB = m_BC
Cm_AB = m_CD = 2/3, while m_BC = 3/2 and m_AD = 1 are not equal
DAC2 = BD2
Solution & Explanation:AB and CD have equal slopes of 2/3, so that pair is parallel. The other opposite sides have slopes 3/2 and 1, which are not equal, so they are not parallel.
Problem 3Difficulty: Mastery
Quadrilateral ABCD has vertices A(-1, 4), B(4, 9), C(8, 5), D(3, 0). Which relationship proves that ABCD is a rectangle using slopes?
AAB2 = BC2 = CD2 = DA2
Bm_AB = m_CD = 1 and m_BC = m_DA = -1
Cm_AB = m_BC = 1
DAC2 = BD2 only
Solution & Explanation:Opposite sides have equal slopes, proving both pairs of opposite sides are parallel. Adjacent slopes 1 and -1 are negative reciprocals, proving a right angle. Together, these prove a rectangle.

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Frequently Asked Questions

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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-GPE.B.6 (Primary standard selected for prompt fields in this prompt cell: CCSS G-GPE.B.6. Skill statement in this prompt cell: Select the slope or distance relationship that proves a geometric claim in the coordinate plane. Associated standards listed with this skill in the curriculum source: CCSS G-GPE.B.6; MA G-GPE.B.6; NY GEO G.G-GPE.B.6. Use this prompt-provided wording as the supporting standard description for this workflow.).

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