Geometry can be one of the most divisive topics that school kids will encounter on their journey from math novice to math expert, ultimately moving on to high school and conquering the SAT. Some students love grabbing their compass, protractor, and various rulers to begin precisely drawing all the shapes and angles they will have learned about thus far. Other students, however, can find geometry difficult, given the skills required that go beyond brain power.
Whether they like it or not, all students are going to have to accept and try to excel at geometry. By the time kids reach grade 7 geometry class, they are introduced to some of the more interesting aspects of geometry, like geometric constructions.
Whether it’s points, lines, and angles, or circles, triangles, and polygons, students will learn to construct them all. The skills developed in geometry classes go far behind the ability to do arithmetic or solve quadratic equations. Students are required to combine the logic and math knowledge acquired so far, and the ability to replicate shapes and lines using new instruments.
Grasping these lessons can be a daunting task, but as you will see here, these topics aren’t always as complicated as some students believe them to be.
Line Segments & Bisectors
First things first. We all know what lines are, but don’t worry, I hear the confused screams, “What is a bisector?”.
A bisector is a line that divides something – such as a line, or an angle – into two equal parts. When we bisect a line, the two parts on either side of the bisector are the line segments.
- Put the compass at one end of the line segment
- Adjust the compass so it’s slightly longer than half the line segment
- Above and below the line, draw arcs using the compass
- Without adjusting the compass, draw arcs from the other end of the line
- Place a ruler where the arcs cross, and draw the bisector.
As you will see from your results, the angle created between a bisector and the line it bisects is 90° or a right angle. This, of course, tells us that the line bisector and the line itself are perpendicular.
We can go one step further than bisecting a line, however. Using the same principles, we can cut a line into N segments. Let’s do another example, where we want to cut a line into three segments. Be sure to check out this video for a visual explanation – utilizing written, visual, and audible learning tools can help you develop a better understanding of the topics.
Cutting a line into three segments:
- Draw a line from the start point, heading somewhat upwards
- Using your compass, divide the line into 3 segments
- Now use your compass to create a parallel line heading backward and down from the endpoint
- Divide this into 3 parts
- Connect the point of intersection of these two new lines
- You will see that where they cross the original line, it will be neatly subdivided.
To ensure we’ve applied the methodology correctly, we can work backward and measure the line segments.
Angles & Bisectors
Line segments aren’t the only creation we can measure, copy, use, and apply to the real world using bisectors. We also use bisectors to segment angles.
Bisecting an angle is no more difficult than bisector a line, and here is a handy video to show you exactly how it should look. Here are the steps involved in constructing an angle bisector using a compass:
- Draw an arc across both rays
- Draw an interior arc
- Draw a second interior arc intersecting the first interior arc
- Draw a line from the vertex to the point where the arcs intersect
As you can see, the process is not too different from that of creating the line segment bisector, and we can also take some different methods to accurately bisect angles, such as using a protractor instead of a compass.
Once we’ve drawn out the angle bisector, we can learn a lot more about that angle and, in turn, that shape, growing our geometry knowledge and positioning ourselves better to deal with these shapes and angles in more detail as we move into high school and beyond.
At Online Math Center, we have the experience and expertise necessary to help your child excel in math class. Whether that be middle school, high school, SAT prep, or competition practice, we cover all bases. On top of that, we offer superior one-to-one tutoring lessons to focus on the topics your child struggles with, and to plug any gaps in their learning that may have developed throughout their time in school.
Contact OMC today to enroll your child in our tutoring classes and see your child go from drawing inaccurate triangles and circles, to successfully bisecting angles and lines, and correctly measuring line segments.