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

GEO.87 Prove triangles similar and use proportional reasoning Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Geometry Math worksheet provides structured practice on GEO.87 Prove triangles similar and use proportional reasoning. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

GEO.87 Prove triangles similar and use proportional reasoning - Primary standard selected for prompt fields in this prompt cell: CCSS G-SRT.B.4-5. Skill statement in this prompt cell: Select the missing step that proves triangles similar and determine the correct value of an unknown length or ratio using proportions. 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.87 Prove triangles similar and use proportional reasoning skill assessments:

Problem 1Difficulty: Mastery

Two bridge braces cross between parallel beams AB and CD, meeting at E. Triangle ABE is compared with triangle CDE. Given AE = 15, CE = 25, BE = 27, and DE = x, which choice gives the missing proof step and x?

AStep: parallel beams make the braces equal, so x = 27

BStep: SSS similarity uses AE/BE = CE/DE; x = 41.7

CStep: the triangles are congruent by vertical angles; x = 15

DStep: vertical angles at E and alternate interior angles from AB parallel to CD prove the triangles similar by AA; x = 45

Solution & Explanation:The vertical angles at E match, and the parallel beams give another angle pair, so AA proves similarity. Corresponding sides give AE/CE = BE/DE, so 15/25 = 27/x. Then x = 45.

Problem 2Difficulty: Mastery

Triangles MNP and QRS are being checked for SSS similarity. Corresponding sides are MN with QR, NP with RS, and MP with QS. Given MN = 14, NP = 21, MP = x, QR = 22, RS = 33, and QS = 55, which choice gives the missing step and the similarity ratio from MNP to QRS?

AStep: the side differences are 8 and 12, so the ratio is 2:3 and x = 37

BStep: AA similarity is needed; ratio = 11:7 and x = 55

CStep: MN/QR = NP/RS = MP/QS, so the triangles are similar by SSS; ratio = 7:11 and x = 35

DStep: two proportional sides prove congruence; ratio = 1:1 and x = 55

Solution & Explanation:The first two ratios are 14/22 = 21/33 = 7/11. Therefore x/55 = 7/11, so x = 35. SSS similarity is proven with ratio 7:11 from MNP to QRS.

Problem 3Difficulty: Mastery

Triangles ABC and DEF have angle A = angle D and angle B = angle E. Side AB = x corresponds to DE = x + 6, and side AC = 16 corresponds to DF = 28. Which choice gives the missing step and x?

AStep: SAS similarity gives x + 6 = 28; x = 22

BStep: two angle pairs prove AA similarity, and x/(x + 6) = 16/28; x = 8

CStep: AA proves congruence, so x = x + 6

DStep: the side ratio should be x/28 = 16/(x + 6); x = 18

Solution & Explanation:The two angle pairs prove similarity by AA. Since AC/DF = 16/28 = 4/7, the corresponding ratio AB/DE is x/(x + 6) = 4/7. Then 7x = 4x + 24, so x = 8.

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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 missing step that proves triangles similar and determine the correct value of an unknown length or ratio using proportions. 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.).