Free Printable WorksheetMathGrade 8Math Curriculum8.G.A.4

8.140 Determining If Two Figures Are Similar Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Grade 8 Math worksheet provides structured practice on 8.140 Determining If Two Figures Are Similar. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

8.140 Determining If Two Figures Are Similar - Which conclusion correctly states whether the two figures are similar? (CCSS 8.G.A.4; CA 8.G.A.4; MA 8.G.A.4)

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

Grade 8

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 8.140 Determining If Two Figures Are Similar skill assessments:

Problem 1Difficulty: Hard

A geometry problem gives Figure L with measurements 2 cm, 3 cm, 4 cm, 5 cm and Figure M with measurements 2 cm, 3 cm, 4 cm, 5 cm. The second figure is just a rotation of the first figure. Which answer is correct?

AFigure L and Figure M are similar because congruent figures are also similar, with a scale factor of 1.

BFigure L and Figure M are not similar because one figure was rotated.

CFigure L and Figure M are not similar because equal side lengths do not count as proportional sides.

DFigure L and Figure M are similar only if the scale factor is greater than 1.

Solution & Explanation:The figures have the same size and shape, so they are congruent. Congruent figures are also similar, and the scale factor from Figure L to Figure M is 1.

Problem 2Difficulty: Hard

Two figures are compared. Figure J is a parallelogram with measurements 4 cm, 6 cm, 4 cm, 6 cm. Figure K is a parallelogram with measurements 4 cm, 6 cm, 4 cm, 6 cm. The second figure is just a rotation of the first figure. Which statement about similarity is true?

AFigure J and Figure K are similar because congruent figures are also similar, with a scale factor of 1.

BFigure J and Figure K are not similar because one figure was rotated.

CFigure J and Figure K are not similar because equal side lengths do not count as proportional sides.

DFigure J and Figure K are similar only if the scale factor is greater than 1.

Solution & Explanation:The figures have the same size and shape, so they are congruent. Congruent figures are also similar, and the scale factor from Figure J to Figure K is 1.

Problem 3Difficulty: Hard

One figure is a regular hexagon with side length 3 cm. The other figure is an equilateral triangle with side length 4.5 cm. Which conclusion is correct?

AThe figures are similar because both are regular and have side lengths 3 cm and 4.5 cm.

BThe figures are not similar because a regular hexagon and a equilateral triangle do not have the same number of sides or the same angle pattern.

CThe figures are similar because regular figures can always be resized into each other.

DThe figures are not similar only because 4.5 is not a multiple of 3.

Solution & Explanation:Regular polygons are similar only when they have the same number of sides and matching angle structure. A regular hexagon and a equilateral triangle do not meet that condition, so they are not similar.

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Grade 8 Math students. It aligns with educational standard 8.G.A.4 (Primary standard selected for prompt fields: CCSS 8.G.A.4. Skill statement: Which conclusion correctly states whether the two figures are similar? Associated standards listed with this skill: CCSS 8.G.A.4; CA 8.G.A.4; MA 8.G.A.4. Use this embedded wording as the best available supporting standard description for this workflow.).