Free Printable WorksheetMathGrade 8Math Curriculum8.G.A.2

8.139 Determining If Two Figures Are Congruent Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Grade 8 Math worksheet provides structured practice on 8.139 Determining If Two Figures Are Congruent. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

8.139 Determining If Two Figures Are Congruent - Which conclusion correctly states whether the two figures are congruent? (CCSS 8.G.A.2; CA 8.G.A.2; MA 8.G.A.2)

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 8.139 Determining If Two Figures Are Congruent skill assessments:

Problem 1Difficulty: Hard

The vertices of pentagon ABCDE are A(-4, 1), B(-1, 2), C(1, 5), D(0, 8), and E(-3, 6). The vertices of pentagon KLMNO are K(-8, 1), L(-2, 2), M(2, 5), N(0, 8), and O(-6, 6). A classmate named Seth says the figures are not congruent because a reflection cannot produce a congruent figure. Which response is the strongest?

ASeth is correct because any figure in a different location is not congruent to the original.

BSeth is correct because congruent figures must have matching coordinates before any motion.

CSeth is incorrect because all figures with unequal area are noncongruent.

DSeth is incorrect because the fact that a reflection cannot produce a congruent figure does not decide congruence; the real issue is that the x-distances were stretched by a factor of 2 while the y-values stayed in the same pattern, so size changed.

Solution & Explanation:The student’s statement needs a better justification. The real reason is that the x-distances were stretched by a factor of 2 while the y-values stayed in the same pattern, so size changed, so no rigid motion works.

Problem 2Difficulty: Hard

Polygon RSTUVW: R(0, 1), S(3, 1), T(3, 2), U(1, 2), V(1, 5), and W(0, 5). Polygon ABCDEF: A(-1, 0), B(-4, 1), C(-4, 0), D(-2, 0), E(-2, -3), and F(-1, -3). Which statement correctly proves that no rigid motion maps the first figure onto the second?

AThey are in different places on the grid.

BThe figures use different vertex letters.

CNo rigid motion can work because after you rotate 180 degrees about the point (-3, 0), then translate 5 units right and 2 units up, vertex R would land at (-1, 1), but the matching vertex A is at (-1, 0).

DOne figure appears turned or flipped.

Solution & Explanation:The correct reason focuses on size and exact matching, not on where the figures sit on the grid. Here, after you rotate 180 degrees about the point (-3, 0), then translate 5 units right and 2 units up, vertex R would land at (-1, 1), but the matching vertex A is at (-1, 0).

Problem 3Difficulty: Hard

On a coordinate plane, pentagon FGHIJ uses the points F(2, 1), G(5, 2), H(7, 5), I(4, 7), and J(1, 4). The image pentagon RSTUV uses the points R(2, 7), S(4, 5), T(7, 3), U(4, 1), and V(1, 4). After plotting the coordinates, Asher claims the figures are not congruent because the figures are in different quadrants. Which answer best evaluates that claim?

AAsher is correct because any figure in a different location is not congruent to the original.

BAsher is incorrect because the fact that the figures are in different quadrants does not decide congruence; the real issue is that after you reflect across the line y = 4, vertex G would land at (5, 6), but the matching vertex S is at (4, 5).

CAsher is correct because congruent figures must have matching coordinates before any motion.

DAsher is incorrect because all figures with unequal area are noncongruent.

Solution & Explanation:Congruence is not about location or labeling; it is about exact matching under rigid motions. Because after you reflect across the line y = 4, vertex G would land at (5, 6), but the matching vertex S is at (4, 5), the claim fails.

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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.2 (Primary standard selected for prompt fields: CCSS 8.G.A.2. Skill statement: Which conclusion correctly states whether the two figures are congruent? Associated standards listed with this skill: CCSS 8.G.A.2; CA 8.G.A.2; MA 8.G.A.2. Use this embedded wording as the best available supporting standard description for this workflow.).