# Common Core Standards: Math

#### The Standards

# High School: Geometry

### Expressing Geometric Properties with Equations HSG-GPE.B.5

**5. Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).**

If you live within driving distance of one of the top five ski resorts in the lower forty-eight, hitting the slopes can be a year round pastime. If you don't, it's still possible to ski year round,

Regardless of their skills on the slopes, we hope students won't experience epic fails when it comes to the slopes. Well, geometric slopes, anyway.

Students are expected to know that lines in the same plane can fall into one of three categories: parallel, perpendicular, or neither. Given two lines, they should be able to prove which of these three categories is applicable. They should also know how to find the equation of a line that is parallel or perpendicular to a given line.

Your students may need a quick refresher on some slope basics. You know, point your toes together, watch out for trees, and don't eat yellow snow. That kind of stuff.

A line's slope, of course, is the ratio of rise over run. In the slope-intercept form of a line's equation, it is the coefficient on the *x* term. Positively sloped lines point up, while negatively sloped ones point down. The greater the magnitude of the slope, the steeper the line.

Parallel lines, or what second graders would refer to as "train track lines," have the same slope and never cross each other. Perpendicular lines, on the other hand, cross at a right angle and feature slopes that are opposite reciprocals of each other.

When your students feel confident enough, tell 'em to grab their boots and poles. Time to hit the slopes!