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Using Similar Triangles to Find Slope

8.EE.B.6
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Aligned To Common Core Standard:

Grade 8 Number System - 8.EE.B.6

How to use Similar Triangles to Find Slope? Kids are introduced to the concept of slope in middle school because it is a bit tricky to understand but is used throughout mathematics. Whether its algebra, calculus, or geometry, the concept of the slope has its applications everywhere. So, what is the slope? The slope is the measurement of the steepness of a line and is also known as the average rate of change. In algebraic terms, it is the rate at which a function is changing. In the majority of the cases, a slope of a line is denoted by "m" and is calculated using the formula; m = (change in "y" variable )/(change in x variable) When a graph runs uphill, we get a positive slope, and when a graph runs downhill, we get a negative slope. When determining the slope of a line, there are a variety of different methods that we can use, and a very useful method is by using the concept of similar triangles. To find the slope of the line through the concept of similar triangles, both triangles have to be right-angled triangles. Start by creating a right triangle from any two points of a line. The vertical line represents a change in y, while the horizontal line represents a change in x. The relationship between the slope of the line and side lengths of triangles is the same between the slope of the line and the lengths of congruent triangles formed. These worksheets will teach students a quick method to determine the slope of a line by inferring from the use of a coordinate graph.

Printable Worksheets And Lessons


  • Slope of Lines Step-by-Step Lesson- Use the triangle method to find the slope of the line. This seems like too much work, but it does give you a definitive answer.

  • Guided Lesson - Write an equation for the graphed line and find the slope using the triangle method.

  • Guided Lesson Explanation - Number one and three take about a page each to explain. It's good to tackle that skill here.

  • Independent Practice - Four full pages of practice work for you here. Equations and slope are all over the place.

  • Matching Worksheet - We have line-a-polooza. Tell us the slope or equation of the lines.




Homework Sheets

Find the slope and equation of a line by using the triangles.

  • Homework 1 - Find the slope of the line using the similar triangles as a guide.
  • Homework 2 - The standard form for the equation of a line is Ax + By = C. A, B and C are real numbers and x and y are variables.
  • Homework 3 - To find the equation of a line this formula is used: (y - y2) = m(x - x2). Both x and y remain variables. The slope, m, will be a real number as well as (x2,y2).



Practice Worksheets

All the three standard skills you will see are here.

  • Practice 1 - Find the slope of the line using the similar triangles as a guide.
  • Practice 2 - Write an equation to represent this graph.
  • Practice 3 - The Y intercept is where the line crosses the Y axis.



Math Skill Quizzes

Quiz one asks you to find the equation of the line. Quiz two focuses on slope and quiz three goes over all skills.

  • Quiz 1 - Write an equation to represent each graph.
  • Quiz 2 - Find the slope of the line using the similar triangles as a guide.
  • Quiz 3 - The equation for a straight line is: y = mx + b m = slope, b = y-intercept. The slope we determined is 1/2.