About This Chapter
How it works:
- Identify the lessons in the Discovering Geometry Using Tools of Geometry chapter with which you need help.
- Find the corresponding video lessons within this online chapter.
- Watch fun videos that cover the using tools of geometry topics you need to learn or review.
- Complete the quizzes to test your understanding.
- If you need additional help, rewatch the videos until you've mastered the material or submit a question for one of our instructors.
Students will learn:
- Geometric constructions
- Midpoint theorem and line segment bisection
- How to design perpendicular lines
- How to construct an angle bisector
- Ways to create a parallel line using a spot not on a line
- Types of geometric construction
- How to draw polygons
- Concurrent lines in triangles
- The construction of circumscribed and inscribed figures
- How to build the median of a triangle
1. Geometric Constructions Using Lines and Angles
Watch this video lesson to learn about geometric construction and how you can copy line segments and angles without using any numbers. All you need is a straight edge and a compass.
2. Line Segment Bisection & Midpoint Theorem: Geometric Construction
Watch this video lesson and you will learn how to bisect a line segment without measurements using just a compass and a straight edge. You'll also learn about the midpoint theorem, which lets you calculate the midpoint if you have the measurements.
3. Constructing Perpendicular Lines in Geometry
In this video lesson, you will see how to use geometric construction to draw perpendicular lines. Learn why geometric construction is useful. Also find out the only two tools in addition to your pencil that you need to do this.
4. Constructing an Angle Bisector in Geometry
Watch this video lesson to learn a cool way to split an angle in half. You can use this method to split a pie slice in half where you can be sure each side is equal.
5. Constructing a Parallel Line Using a Point Not on the Given Line
Watch this video lesson, and you will learn how to draw parallel lines with just a compass and a straightedge. Also, learn why you would want to be able to do this in real life.
6. Constructing Triangles: Types of Geometric Construction
When you're asked to construct a triangle, it's time to break out that compass and straight edge! In this lesson, find out how to construct triangles no matter what you're given.
7. Constructing Similar Polygons
This lesson will teach you how to construct similar polygons, which are very useful in many quantitative fields. You'll learn that all of this has something to do with, of all things, snowflakes!
8. Properties of Concurrent Lines in a Triangle
Centroids, orthocenters, incenters, circumcenters, oh my! Don't worry though. In this lesson, we master the various terms for concurrent lines in triangles and match them to altitudes, angle bisectors, perpendicular bisectors and medians.
9. Inscribed and Circumscribed Figures: Definition & Construction
A square and a circle may be different shapes, but they still can have a unique relationship. In this lesson, we'll learn about inscribed and circumscribed figures.
10. Constructing the Median of a Triangle
If you have one triangle and want to divide it, you can use a median line. Medians have special geometric properties that we'll learn about in this lesson.
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Other chapters within the Discovering Geometry An Investigative Approach: Online Help course
- Discovering Geometry Chapter 1: Introducing Geometry
- Discovering Geometry Chapter 2: Reasoning in Geometry
- Discovering Geometry Chapter 4: Discovering and Proving Triangle Properties
- Discovering Geometry Chapter 5: Discovering and Proving Polygon Properties
- Discovering Geometry Chapter 6: Discovering and Proving Circle Properties
- Discovering Geometry Chapter 7: Transformations and Tessellations
- Discovering Geometry Chapter 8: Area
- Discovering Geometry Chapter 9: The Pythagorean Theorem
- Discovering Geometry Chapter 10: Volume
- Discovering Geometry Chapter 11: Similarity
- Discovering Geometry Chapter 12: Trigonometry
- Discovering Geometry Chapter 13: Geometry as a Mathematical System