# Points, Lines, Angles, and Planes

# Topics Exercises

#### Collinearity

Sample ProblemHow many ways are there to draw a segment on a piece of paper with both endpoints at corners of the page?First, we'll make each of the corners a point, giving them names like...

#### Angles

When two lines cross, not only do they meet at exactly one point, but they form four corners as well. For example, when you text, "Spotted: N and S looking cozy at 2nd and 74th—do I see a...

#### Length and Measurement

What happens when segments and angles stop being polite, and start getting real? Step back, Jersey Shore. There's a new reality show in town. As fascinating as a geometry-themed TV series sounds, w...

#### Arithmetic in Geometry

Say you're going to school, and you plan on stopping by Taco Bell on the way. Your house, Taco Bell, and school are all on the same street, and Taco Bell is between you and school. They're collinea...

#### Algebra in Geometry

You thought you were done with algebra. Unfortunately, math continually builds upon itself like an endless dance of the Hokey Pokey, and Geometry is no exception. Now shake it all about.We might be...

#### Planes

A plane is like an infinitely big sheet of paper that continues forever in all directions. It's sort of like a single slice of the three-dimensional world in the same way that a line is like a sing...

#### Distance and Midpoint Formulas

Slapping coordinates on a line makes any line look like the number line. Just the same, this system of coordinates can make any plane look like the x-y plane from algebra.Since lines only requir...