Free Printable WorksheetMathGeometryMath CurriculumG-SRT.B.4-5

GEO.89 Angle bisector theorem Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Geometry Math worksheet provides structured practice on GEO.89 Angle bisector theorem. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

GEO.89 Angle bisector theorem - Primary standard selected for prompt fields in this prompt cell: CCSS G-SRT.B.4-5. Skill statement in this prompt cell: Select the correct proportion from the angle bisector theorem and determine an unknown segment length. Associated standards listed with this skill in the curriculum source: CCSS G-SRT.B.4-5; NY GEO G.G-SRT.B; MA G-SRT.B; FL MA.912.GR.1.2, 1.6; CCSS G-CO.C.10; FL MA.912.GR.1.3; MA G-CO.C.10; NY GEO G.G-CO.C.10; 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.89 Angle bisector theorem skill assessments:

Problem 1Difficulty: Mastery
In triangle XYZ, XW bisects angle X and meets YZ at W. XY = 4t + 18, XZ = 5t, YW = 30, and WZ = 24. What is XY?
AXY = 42
BXY = 46
CXY = 50
DXY = 54
Solution & Explanation:The segment ratio is YW/WZ = 30/24 = 5/4, so (4t + 18)/(5t) = 5/4. Cross multiplication gives 16t + 72 = 25t, so t = 8. Therefore XY = 4(8) + 18 = 50.
Problem 2Difficulty: Mastery
A roof truss is modeled by a triangle. A brace bisects the top angle and meets the base beam. The two slanted sides of the top angle are 45 ft and 60 ft, and the base beam is 63 ft long. What is the longer base segment?
A27 ft
B31.5 ft
C36 ft
D42 ft
Solution & Explanation:The side ratio is 45:60 = 3:4, so the base is divided in the ratio 3:4. Since 63/(3 + 4) = 9, the longer segment is 4(9) = 36 ft.
Problem 3Difficulty: Mastery
In triangle ABC, AD bisects angle A. AB = 25, AC = 35, and BC = 72. A claim says BD = 30 and DC = 42. Which statement is correct?
AThe claim is consistent because 25/35 = 30/42 and 30 + 42 = 72.
BThe claim is inconsistent because an angle bisector must divide the base equally.
CThe claim is inconsistent because the side ratio should be 35/25 only.
DThe claim is consistent only if BC = 70.
Solution & Explanation:The side ratio is 25/35 = 5/7. The proposed segment ratio is 30/42 = 5/7, and 30 + 42 = 72. The claim is consistent with the theorem.

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Frequently Asked Questions

Common questions about printing, using, and solving this worksheet

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QIs this GEO.89 Angle bisector theorem worksheet free for teachers and homeschoolers?

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Yes! In addition to this printable worksheet, students can practice GEO.89 Angle bisector theorem 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-SRT.B.4-5 (Primary standard selected for prompt fields in this prompt cell: CCSS G-SRT.B.4-5. Skill statement in this prompt cell: Select the correct proportion from the angle bisector theorem and determine an unknown segment length. Associated standards listed with this skill in the curriculum source: CCSS G-SRT.B.4-5; NY GEO G.G-SRT.B; MA G-SRT.B; FL MA.912.GR.1.2, 1.6; CCSS G-CO.C.10; FL MA.912.GR.1.3; MA G-CO.C.10; NY GEO G.G-CO.C.10; TEKS §111.41(c). Use this prompt-provided wording as the supporting standard description for this workflow.).

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