Radicals, Lines, Planes, & More | It All Adds Up

Screen Shot 2017-08-22 at 10.59.09 AMWelcome to the all-new edition of It All Adds Up! I’ve redesigned one of 12 and Beyond’s original series, and made it better and easier to understand!

For more details about what you can expect this Fall, check out the Global Interests page at the top of this post. In this post, I’ll be covering radicals, lines, planes, as well as providing additional opportunities for researchRead on for more!

I gave myself a few weeks of leeway before starting It All Adds Up again so I could get acclimated to High School, but I quickly realized, being in all honors classes, things move very fast. In the first week of school, we learned about simplifying, adding, subtracting, multiplying, dividing, and rationalizing radicals. That’s today’s main lesson. However, after that one week, we started to really venture out into the world of geometry. Unfortunately, I can’t cover everything in one post. So, if you’d like to do your own research, here’s what else we have been working on:

  • lines, points, and planes (brief lesson at end of post), naming of lines, points, planes
  • line segments, segment addition postulate, congruent segments
  • segment bisectors, finding missing midpoints & endpoints, Midpoint Formula, Distance Formula, finding lengths of line segments
  • classifying angles, angle addition postulate, angle bisectors, congruent angles
  • complementary, supplementary, and adjacent angles, linear pairs, opposite rays
  • classifying polygons, concave & convex polygons
  • finding the perimeter/circumference, and area, of shapes (formulas)

I’m giving you that list so I can skip over those topics in future editions, so that 12 and Beyond and school are in line, and not behind.


For this edition, I compiled everything you need to know into one graphic:

Screen Shot 2017-09-28 at 6.18.06 PM.png

Lines, Points, & Planes

I’m sure you are aware of what a line and point are. A plane is a two dimensional surface that contains points, lines, etc. and extends without end. When we draw one, we usually draw it as a quadrilateral. For example, this is a plane:

Screen Shot 2017-09-28 at 6.36.30 PM.png

The letters represent individual points. For today, I want to go over two terms:

Colinnear points: points that lies on the same line. Points A and B are collinear. A and D are not.

Coplanar points: points that lie within the same plane. Points B, E, Z, H, A, and D are in plane P, so they are coplanar. If a point was placed outside of the blue plane, or if a line extended beyond the plane, it would not be considered coplanar.

Want to extend this lesson even more? Google naming lines and planes.

I hope I am not being overwhelming- if you have any questions about this content, feel free to ask me in the contents.

Thanks so much for reading! Another It All Adds Up post releases in two weeks.


One thought on “Radicals, Lines, Planes, & More | It All Adds Up

  1. Pingback: It All Adds Up Sample Problems: Radicals, Lines, Planes, & More – 12 and Beyond

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