In this lesson, students connect their previous work with slope and parallel lines to show that non-vertical parallel lines have equal slopes. They begin by noticing that the slopes of translated lines are equal and recalling that translated lines are parallel. Then they deconstruct a proof of the slope criterion for parallel lines and explain each step. In this process, they are taking a compact mathematical statement and constructing a viable argument to communicate the ideas more clearly to themselves and their peers (MP3). Once students are convinced that parallel lines have equal slopes, they apply this theorem to write equations and prove that a quadrilateral is a parallelogram.

Technology isn't required for this lesson, but there are opportunities for students to choose to use appropriate technology to solve problems. We recommend making technology available.