About This Chapter
Honors Geometry: Relationships Within Triangles- Chapter Summary
As you study relationships with triangles, you will start to understand more concepts within geometry. By the time you've completed these lessons, you'll be able to do the following:
- Understand the midsegment theory
- Know what the orthocenter in geometry is
- Explain triangle inequalities
- Recall what the centroid is
|Midsegment: Theorem & Formula||Discover what the midsegment theorems are and how they can be used.|
|Segment Bisector: Definition & Example||Understand the different types of segment bisectors.|
|Constructing the Median of a Triangle||Learn how to use a median line in a triangle.|
|Centroid: Definition, Theorem & Formula||Identify how to locate the centroid of a triangle.|
|Orthocenter in Geometry: Definition & Properties||Discover what the orthocenter is and how to graph it.|
|Triangle Inequality: Theorem & Proofs||Take a look at the triangle inequality theorems.|
|Inequalities in One Triangle||Solve inequalities in one triangle.|
|Inequality Theorems for Two Triangles||Learn how to solve inequalities in two triangles.|
|Congruence in Overlapping Triangles||See if you can prove if overlapping triangles are congruent.|
1. Midsegment: Theorem & Formula
Learn about the midsegment of a triangle and the way in which it's found. Read about the properties of the midsegment as they relate to the base, angles, perimeter and area, and then test your knowledge with a short quiz.
2. Segment Bisector: Definition & Example
This lesson explains types of segment bisectors and demonstrates examples of segment bisectors. We will also review the definitions of some key vocabulary words.
3. 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.
4. Centroid: Definition, Theorem & Formula
Have you ever wondered how to find the balancing point of a triangle? The answer can be found in this lesson on the centroid of a triangle! We'll learn how medians are used to locate the centroid and then discuss its various properties.
5. Orthocenter in Geometry: Definition & Properties
This lesson involves a well-known center of a triangle called the orthocenter. Its definition and properties will be discussed, and an example will be worked showing how to find its location on a graph.
6. Triangle Inequality: Theorem & Proofs
In this lesson, we will use definitions and proofs to learn what the triangle inequality theorem is, why it works, and how to use it to determine if three given line segments can form a triangle.
7. Inequalities in One Triangle
Triangles show up all the time in the world around us. This lesson discusses some of the inequalities that describe the lengths of the sides of a triangle and the measurements of the angles. We'll look at theorems, proofs, and applications involving these inequalities.
8. Inequality Theorems for Two Triangles
Watch this lesson to learn about two inequality theorems that can help you compare two triangles to each other. You'll also go through some practice problems with complete explanations.
9. Congruence in Overlapping Triangles
This lesson provides an introduction to determining if triangles that overlap are congruent to each other. It also defines congruent triangles and explains the five ways to prove triangles congruent.
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Other chapters within the Honors Geometry Textbook course
- Honors Geometry: Foundations of Geometry
- Honors Geometry: Fundamentals of Geometry Proofs
- Honors Geometry: Logic in Mathematics
- Honors Geometry: Introduction to Geometric Figures
- Honors Geometry: Properties of Triangles
- Honors Geometry: Similar & Congruent Triangle Proofs
- Honors Geometry: Right Triangle Proofs
- Honors Geometry: Parallel Lines & Polygons
- Honors Geometry: Parallel Line Proofs
- Honors Geometry: Coordinate Geometry
- Honors Geometry: Analytical Geometry
- Honors Geometry: Similar Polygons
- Honors Geometry: Properties of Polygons & Circles
- Honors Geometry: Polygons & Quadrilaterals
- Honors Geometry: Circular Arcs & Circles
- Honors Geometry: Conic Sections
- High School Geometry: Geometric Solids
- Honors Geometry: Introduction to Trigonometry
- Honors Geometry: Right Triangles & Trigonometry
- Honors Geometry: Area, Surface Area & Volume
- Honors Geometry: Perimeter & Circumference
- Honors Geometry: Transformations
- Honors Geometry: Matrices