In previous courses, students studied slopes of lines, and in previous units, students studied parallel lines. In this lesson, students connect these ideas and prove that non-vertical parallel lines have equal slopes. They begin class by noticing 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 (MP3) to communicate the ideas more clearly to themselves and their peers. Once students are convinced parallel lines have equal slopes, they apply this theorem to write equations and prove 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.
- Prove the slope criterion for parallel lines and use it to solve geometric problems.
- Let’s investigate parallel lines in the coordinate plane.
- I can prove that the slopes of parallel lines are equal.
- I can use slopes of parallel lines to solve problems.
The form of an equation for a line with slope \(m\) through the point \((h,k)\). Point-slope form is usually written as \(y-k = m(x-h)\). It can also be written as \(y = k + m(x-h)\).