Math 1 · Unit 4
Parallel and Perpendicular Lines
Four lessons: parallel lines share a slope, perpendicular lines and the negative reciprocal, sorting any two lines as the same, parallel, or perpendicular, and using slopes to check shapes. It is all one idea, the slope, doing two new jobs. Each card below opens a lesson. Every lesson has practice with hints, a study guide, a worksheet with an answer key, and a lesson plan.
Parallel Lines Share a Slope
Parallel lines never cross because they have the same slope and different y-intercepts: same m, different b. It is the family of lines again, slid up or down. Decide whether two lines are parallel, then write a parallel line through a point by keeping m and finding b.
Start Unit 4, Lesson 1Perpendicular Lines and the Negative Reciprocal
Perpendicular lines cross at a square corner. Turn a line a quarter turn and the rise and run trade places, so the new slope is the negative reciprocal: flip the fraction and change the sign. Product of the slopes: negative one. See it move in the explorer, then write a perpendicular line through a point.
Start Unit 4, Lesson 2Same, Parallel, or Perpendicular?
Both slope jobs together. Compare two slopes: equal means parallel (or the same line if b matches too), product of negative one means perpendicular, anything else is neither. Sort pairs of lines, then choose the right move to write a parallel or perpendicular line through a point.
Start Unit 4, Lesson 3Using Slopes to Check Shapes
Put slope to work proving things. From the corners of a shape, compute the slopes of its sides: equal slopes mean parallel sides, slopes that multiply to negative one mean a right angle. Enough to prove a rectangle or a right triangle with algebra alone. Equal side lengths wait for distance in Unit 11.
Start Unit 4, Lesson 4Printables for Unit 4
Study guides, worksheets with answer keys, and lesson plans for every lesson in this unit.