About This Chapter
Honors Geometry: Similar & Congruent Triangle Proofs - Chapter Summary and Learning Objectives
Triangles can be seen as similar just by looking at them, but using mathematically proven formulas will make your studies much easier. These lessons contain a number of proofs that verify similarity and congruence in triangles that will appear in your geometry problems and on graphs. Topics you'll look at include the following:
- How to use the AAS Theorem
- How to utilize the Perpendicular Bisector Theorem
- What the Triangle Congruence Postulates are
- How to prove relationships in congruence and similarity
- What the properties are for concurrent triangle lines
|Triangle Proportionality Theorem||Understand how to use this theorem to solve problems involving triangles.|
|How to Identify Similar Triangles||Learn to recognize triangle traits.|
|Applications of Similar Triangles||Apply knowledge of similar triangles to solve problems.|
|Congruence Proofs: Corresponding Parts of Congruent Triangles||Find similar parts of triangles using congruence proofs.|
|The AAS (Angle-Angle-Side) Theorem: Proof and Examples||Use the AAS Theorem to find congruency.|
|Perpendicular Bisector Theorem: Proof and Example||See how to divide lines into equal halves with this theorem.|
|Angle Bisector Theorem: Proof and Example||Study examples of this theorem and see how it works.|
|Triangle Congruence Postulates: SAS, ASA & SSS||Compare the three postulates and find out how they each prove congruency.|
|The Transitive Property of Similar Triangles||Discover how this property is used with similar triangles.|
|Congruence of Isosceles Triangles: Proving the Theorem||Learn to prove this theorem as well as its converse.|
|Similarity Transformations in Corresponding Figures||Take a look at how to transform similar figures.|
|How to Prove Relationships in Figures using Congruence & Similarity||Use what you have learned to prove relationships geometrically.|
|Practice Proving Relationships using Congruence & Similarity||Apply skills you've gained with practice problems.|
|Properties of Concurrent Lines in a Triangle||Review terms related to concurrent lines.|
1. Triangle Proportionality Theorem
Watch this video lesson to learn all about the triangle proportionality theorem and how you can use this interesting theorem to help you solve problems. Learn how a parallel line can create sides that are proportional to each other.
2. How to Identify Similar Triangles
Similar triangles have the same characteristics as similar figures but can be identified much more easily. Learn the shortcuts for identifying similar triangles here and test your ability with a quiz.
3. Applications of Similar Triangles
Similar triangles are used to solve problems in everyday situations. Learn how to solve with similar triangles here, and then test your understanding with a quiz.
4. Congruence Proofs: Corresponding Parts of Congruent Triangles
Congruent triangles have congruent sides and angles, and the sides and angles of one triangle correspond to their twins in the other. In this lesson, we'll try practice with some geometric proofs based around this theorem.
5. The AAS (Angle-Angle-Side) Theorem: Proof and Examples
When trying to find out if triangles are congruent, it's helpful to have as many tools as possible. In this lesson, we'll add to our congruence toolbox by learning about the AAS theorem, or angle-angle-side.
6. Perpendicular Bisector Theorem: Proof and Example
Perpendicular bisectors are multifunctional lines. They're not only perpendicular to the line in question, they also neatly divide it into two equal halves. In this lesson, we'll learn about the perpendicular bisector theorem.
7. Angle Bisector Theorem: Proof and Example
The angle bisector theorem sounds almost too good to be true. In this lesson, we set out to prove the theorem and then look at a few examples of how it's used.
8. Triangle Congruence Postulates: SAS, ASA & SSS
When we have two triangles, how can we tell if they're congruent? They may look the same, but you can be certain by using one of several triangle congruence postulates, such as SSS, SAS or ASA.
9. The Transitive Property of Similar Triangles
Watch this video lesson and you will understand what the transitive property is and how it applies to similar triangles. Watch as we apply the transitive property to three similar triangles.
10. Congruency of Isosceles Triangles: Proving the Theorem
Isosceles triangles have two equal sides. Are the base angles also equal? In this lesson, we'll prove how this is true. We'll also prove the theorem's converse.
11. Similarity Transformations in Corresponding Figures
Watch this video lesson to learn how you can tell if two figures are similar by using similarity transformations. Learn how to find the corresponding sides and angles and then how to compare them.
12. How to Prove Relationships in Figures using Congruence & Similarity
In this lesson, we'll look at similar and congruent figures and the properties that they hold. We will then look at how to use these properties to prove relationships in these figures in various examples.
13. Practice Proving Relationships using Congruence & Similarity
In geometry, if two shapes are similar they have the same shape but different sizes, while two congruent shapes have the same shape and size. In this lesson, you will learn how to prove that shapes are similar or congruent.
14. 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.
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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: Right Triangle Proofs
- Honors Geometry: Relationships Within Triangles
- 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