Free Printable WorksheetMathGrade 8Math Curriculum8.EE.B.6

8.52 Using Similar Triangles to Explain Slope Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Grade 8 Math worksheet provides structured practice on 8.52 Using Similar Triangles to Explain Slope. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

8.52 Using Similar Triangles to Explain Slope - Which explanation correctly uses similar right triangles to justify that a line's slope is constant? (CCSS 8.EE.B.6; CA 8.EE.B.6; MA 8.EE.B.6)

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 8.52 Using Similar Triangles to Explain Slope skill assessments:

Problem 1Difficulty: Hard
For any value of a, the points (a, 2a + 1) and (a + 6, 2a + 9) lie on the same line. Similar triangles on the line show a constant slope. What is the slope?
Solution & Explanation:The rise from the first point to the second is (2a + 9) - (2a + 1) = 8. The run is (a + 6) - a = 6. So the slope is 8/6 = 4/3.
Problem 2Difficulty: Hard
A line has y-intercept -3. For every point (x, y) on the line, similar triangles show that (y + 3)/x = 5/4. Which equation represents the line?
Ay = (5/4)x - 3
By = (4/5)x - 3
Cy = (5/4)x + 3
Dy = (-5/4)x - 3
Solution & Explanation:If (y + 3)/x = 5/4, then y + 3 = (5/4)x. Subtract 3 to get y = (5/4)x - 3.
Problem 3Difficulty: Hard
One right triangle on a line has rise n + 1 and run 2n + 2. Another has rise 3 and run 6. Which statement is correct for every n > -1?
AThey represent the same slope for every n > -1 because both ratios simplify to 1/2.
BThey represent the same slope only when n = 1.
CThey never represent the same slope because one ratio contains a variable.
DThey represent opposite slopes because the numbers are written differently.
Solution & Explanation:The first ratio simplifies to (n + 1)/(2n + 2) = 1/2, and the second ratio is 3/6 = 1/2. Since the ratios match, they represent the same slope.

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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.EE.B.6 (Primary standard selected for prompt fields: CCSS 8.EE.B.6. Skill statement: Which explanation correctly uses similar right triangles to justify that a line's slope is constant? Associated standards listed with this skill: CCSS 8.EE.B.6; CA 8.EE.B.6; MA 8.EE.B.6. Use this embedded wording as the best available supporting standard description for this workflow.).

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