# Consistency Of Slope Using Similar Triangles Math Games

In this series of games, your students will learn to use similar triangles to explain why the slope is the same between any two distinct points on a non-vertical line. The Consistency Of Slope Using Similar Triangles learning objective — based on CCSS and state standards — delivers improved student engagement and academic performance in your classroom, as demonstrated by research. This learning objective directly references 8.EE.B.6 as written in the common core national math standards.

Scroll down for a preview of this learning objective’s games and the concepts.

## Concepts Covered

Plotting points on the coordinate plane, in which each axis is marked with a scale representing one quantity, provides a visual representation of the relationship between two quantities where the slope is the unit rate. The ratio between the rise and run for any two points on the line is always the same. Similar right triangles with the same hypotenuse (slope) and angles have the same ratio of the legs (rise and run).

For a line through the origin, the right triangle whose hypotenuse is the line segment from (0, 0) to a point (x, y) on the line is similar to the right triangle from (0, 0) to the point (1, m) on the line. The equation for a line not through the origin can be derived in a similar way, starting from the y-intercept (0, b) instead of the origin (y =mx + b where b is the y-intercept).

A preview of each game in the learning objective is found below.

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