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

GEO.86 Similarity criteria for triangles Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Geometry Math worksheet provides structured practice on GEO.86 Similarity criteria for triangles. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

GEO.86 Similarity criteria for triangles - Primary standard selected for prompt fields in this prompt cell: CCSS G-SRT.B.4-5. Skill statement in this prompt cell: Select the similarity criterion that applies to two triangles based on given angle measures and proportional side lengths. 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. 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.86 Similarity criteria for triangles skill assessments:

Problem 1Difficulty: Mastery

Triangles ABC and DEF have corresponding vertices in the order named. AB=9, BC=12, DE=12, EF=16, angle B=64 degrees, and angle E=65 degrees. No third side or second angle pair is given. Which criterion applies?

ANo similarity criterion applies; the two side ratios match, but the included angles are not congruent.

BAA similarity; this would require two corresponding angle pairs.

CSAS similarity; this would require two corresponding side ratios with the included angle.

DSSS similarity; this would require all three corresponding side ratios.

Solution & Explanation:The ratios 9/12 and 12/16 both equal 3/4, but SAS requires the included angles to be equal. Since angle B is 64 degrees and angle E is 65 degrees, no similarity criterion applies.

Problem 2Difficulty: Mastery

A diagram with parallel lines shows two triangles. The first triangle has marked angles 64 degrees and 46 degrees. The second triangle has matching corresponding angles 64 degrees and 46 degrees created by the parallel lines. Which criterion applies?

ASSS similarity; this would require all three corresponding side ratios.

BNo similarity criterion applies; this would mean the facts do not complete AA, SAS, or SSS.

CAA similarity; two corresponding angle pairs, 64 degrees and 46 degrees, match.

DSAS similarity; this would require two corresponding side ratios with the included angle.

Solution & Explanation:The parallel lines create matching corresponding angles. Since the two triangles each have 64-degree and 46-degree angles, AA similarity applies.

Problem 3Difficulty: Mastery

In a diagram, two triangles share vertical angles at point O. Along one line, OA=5 and OD=12.5. Along the other line, OB=8 and OE=20. Which criterion applies to triangles AOB and DOE?

ASAS similarity; 5/12.5 = 8/20 and the vertical angles at O are congruent and included.

BSSS similarity; this would require all three corresponding side ratios.

CNo similarity criterion applies; this would mean the facts do not complete AA, SAS, or SSS.

DAA similarity; this would require two corresponding angle pairs.

Solution & Explanation:The two side ratios both equal 0.4, and the included angles at O are vertical angles, so they are congruent. This proves similarity by SAS.

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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-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 similarity criterion that applies to two triangles based on given angle measures and proportional side lengths. 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. Use this prompt-provided wording as the supporting standard description for this workflow.).