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Geometry: High School15 chapters | 160 lessons

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Lesson Transcript

Instructor:
*Kevin Newton*

Kevin has edited encyclopedias, taught middle and high school history, and has a master's degree in Islamic law.

There are a number of tools available to geometry students to help make their work a bit easier. In this lesson, we will review how to use many of them in order for you to get the most out of every geometry class.

One of the truly great things about geometry is that it deals with shapes that you can actually see and manipulate. Is it as fun as playing with counting blocks as a kid when you were first learning to count? Probably not. However, it does beat always trying to find the value of *x* - the pesky thing keeps changing! But in geometry, you get to learn about important things - like how to find the area of a rectangular room or how much paint you'd need to cover a triangular shape on the side of your suitcase. With that practicality also comes the opportunity to draw things out. In this lesson, we're going to focus on how to best use the various tools available to us in geometry to make sure our diagrams are as accurate as possible.

When making diagrams in geometry class, the most basic tools that you'll find yourself using are **rulers** and straight edges. Often, these are combined in the same tool, but they are useful nonetheless. Chances are that you know how to draw a line using either, but if you don't, simply trace along the edge.

However, I didn't bring rulers up to just mention how to draw a line. Instead, think about how you'd draw two parallel lines. Now things get a little bit more interesting. To draw a parallel line, first draw a line that you want the parallel line relative to. Now, measure two spots above or below that line, making sure that both are either above or below. However, be sure that the two spots are the same distance away. This is the distance that you want the lines to be apart from one another. Now connect the two lines with a new line, drawn with the ruler or straight edge. As a result, you now have two parallel lines. You can repeat this process as needed if you require additional lines parallel to that first segment.

What if you need perpendicular lines, or lines drawn at a certain angle? You can't just use a ruler to make those lines. Instead, you'll need a **protractor**. A protractor is a half-circle instrument used to measure angles. To use a protractor to draw a perpendicular line, put the base line of the protractor across the line that you are trying to draw a perpendicular line relative to. Make sure that it is the base line within the protractor, signaled by a line running along the edge about a half an inch inside the metal or plastic, and not the base of the protractor itself.

Using your pencil or pen, make a mark on the line at the origin point, then make an additional point at the 90-degree mark. Then simply connect the two points with a straight edge. For a line at a different angle, simply follow the above procedure but instead of 90 degrees, choose whatever angle is appropriate.

Rulers are useful for lines, and protractors can make short work of polygons, but what about circles? If you've ever taken an art class, you've probably heard how difficult it is to draw a perfect circle freehand. Luckily for us, you have a tool to help in geometry. It is called a **compass**. It is a V-shaped tool that has a pencil at one leg and a needle at the other. Many compasses allow you to measure out the radius of the circle at the top of the compass and put the needle at the center point. Otherwise, you'll have to use a ruler to measure the distance from the needle to the pencil for the radius of the circle you wish to draw. From there it is simply a matter of rotating the compass.

But what if you have to make a circle bigger than the compass can allow? In that case, you just need a string! Measure out a piece of string to the desired length, then attach one edge to the pencil and the other to the middle of the circle. Trace out the shape and you're done!

In this lesson we learned how to use tools common to any geometry class to better sketch the shapes that we are learning about. We saw how **rulers** and straight edges could be used to make straight lines as well as parallel lines. We then used **protractors** to make perpendicular lines as well as angles for triangles and other polygons. Finally, we used both a **compass** and a string to draw nearly perfect circles without the frustration of stopping and trying again using only freehand techniques.

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Geometry: High School15 chapters | 160 lessons

- Line Segments & Rays: Definition & Measurement 3:59
- Types of Angles: Vertical, Corresponding, Alternate Interior & Others 10:28
- Geometric Constructions Using Lines and Angles 4:32
- Line Segment Bisection & Midpoint Theorem: Geometric Construction 4:39
- Dividing Line Segments into Equal Parts: Geometric Construction 5:22
- Parallel, Perpendicular and Transverse Lines 6:06
- Constructing Perpendicular Lines in Geometry 3:39
- Constructing an Angle Bisector in Geometry 3:36
- Methods & Tools for Making Geometric Constructions 3:17
- Practice Making Geometric Constructions with Tools 4:17
- Go to High School Geometry: Introduction to Geometric Figures

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