# Ch 37: 8th Grade Math: Triangle Theorems and Proofs in Geometry

### About This Chapter

## 8th Grade Math: Triangle Theorems and Proofs in Geometry - Chapter Summary

Each video lesson is about five minutes long and is designed to help your 8th graders remember the triangle theorems and proofs you have introduced in class. The fun and light-hearted videos examine postulates, proofs, and theorems of triangles using angles, hypotenuses and sides and show students how to apply these to solve geometric problems. You can use the multiple-choice quizzes to see where students may have questions, and the chapter exam can test what they have remembered from this chapter.

## Chapter Lessons and Objectives

Lesson | Objective |
---|---|

Applications of Similar Triangles | Students examine ways to solve applications of similar triangles. |

Triangle Congruence Postulates: SAS, ASA & SSS | Students look at examples of SAS, ASA and SSS postulates to solve the congruence of two triangles. |

Congruence Proofs: Corresponding Parts of Congruent Triangles | Instructors provide problems in which students apply the corresponding parts of congruent triangles proof. |

Converse of a Statement: Explanation and Example | Students learn that to use the converse of a statement as a reason in any proof, it must first be true. |

Similarity Transformations in Corresponding Figures | With this lesson, students determine if two given figures are similar by using the definition of similarity in terms of similarity transformations. |

Proving Relationships in Figures using Congruence and Similarity | Lesson leads students to apply congruence and similarity of triangles to prove relationships in geometric figures. |

Practice Proving Relationships | Students have a chance to practice solving problems that prove relationships. |

The AAS (Angle-Angle-Side) Theorem: Proof and Examples | Students discover what the angle-angle-side theorem states and how to prove it. |

The HA (Hypotenuse Angle) Theorem: Proof, Explanation & Examples | Instructors explain the hypotenuse angle theorem. |

The HL (Hypotenuse Leg) Theorem: Definition, Proof & Examples | In this lesson, students gather information about the hypotenuse leg theorem. |

Perpendicular Bisector Theorem: Proof and Example | Students learn the segment bisector theorem by looking at an example a perpendicular bisector of a given line segment. |

Angle Bisector Theorem: Proof and Example | Lesson builds on the previous lesson and uses the bisector of a given angle to prove the bisector theorem. |

Congruency of Right Triangles: Definition of LA and LL Theorems | Students examine the LA and LL theorems. |

Congruency of Isosceles Triangles: Proving the Theorem | Students learn that when the base angles of an isosceles triangle are congruent, the angles opposite these sides are also congruent. |

### 1. 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.

### 2. 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.

### 3. 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.

### 4. Converse of a Statement: Explanation and Example

Just because a conditional statement is true, is the converse of the statement always going to be true? In this lesson, we'll learn the truth about the converse of statements.

### 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. The HA (Hypotenuse Angle) Theorem: Proof, Explanation, & Examples

In this lesson, we'll learn about the hypotenuse angle theorem. With this theorem, we can prove two right triangles are congruent with just congruent hypotenuses and acute angles.

### 7. The HL (Hypotenuse Leg) Theorem: Definition, Proof, & Examples

In this lesson, we'll learn about the hypotenuse leg theorem. This theorem enables us to prove two right triangles are congruent based on just two sides.

### 8. 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.

### 9. 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.

### 10. Congruency of Right Triangles: Definition of LA and LL Theorems

In this lesson, we'll learn two theorems that help us prove when two right triangles are congruent to one another. The LA theorem, or leg-acute, and LL theorem, or leg-leg, are useful shortcuts for proving congruence.

### 11. 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.

### Earning College Credit

Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

### Transferring credit to the school of your choice

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

### Other Chapters

Other chapters within the 8th Grade Math: Practice & Review course

- 8th Grade Math: Basic Arithmetic Operations
- 8th Grade Math: Divisibility
- 8th Grade Math: Number Properties
- 8th Grade Math: Number Theory
- 8th Grade Math: Factoring
- 8th Grade Math: Estimation and Rounding
- 8th Grade Math: Whole Numbers
- 8th Grade Math: Simplifying Whole Number Expressions
- 8th Grade Math: Negative Numbers
- 8th Grade Math: Absolute Value
- 8th Grade Math: Integers
- 8th Grade Math: Rational Numbers
- 8th Grade Math: Inequalities
- 8th Grade Math: Introduction to Decimals
- 8th Grade Math: Operations with Decimals
- 8th Grade Math: Introduction to Fractions
- 8th Grade Math: Operations with Fractions
- 8th Grade Math: Percents
- 8th Grade Math: Exponents & Exponential Expressions
- 8th Grade Math: Roots & Radical Expressions
- 8th Grade Math: Basic Algebraic Expressions
- 8th Grade Math: Algebraic Distribution
- 8th Grade Math: Simplifying & Solving Rational Expressions
- 8th Grade Math: The Coordinate Graph
- 8th Grade Math: Linear Equations
- 8th Grade Math: Systems of Linear Equations
- 8th Grade Math: Properties of Functions
- 8th Grade Math: Graphing Functions
- 8th Grade Math: Solving Math Word Problems
- 8th Grade Math: Introduction to Geometric Figures
- 8th Grade Math: Triangles in Geometry
- 8th Grade Math: Quadrilaterals in Geometry
- 8th Grade Math: Circles in Geometry
- 8th Grade Math: Circular Arcs & Measurement in Geometry
- 8th Grade Math: Polyhedrons and Geometric Solids
- 8th Grade Math: Symmetry, Similarity & Congruence in Geometry
- 8th Grade Math: Similar Polygons in Geometry
- 8th Grade Math: The Pythagorean Theorem in Geometry
- 8th Grade Math: Units of Measurement
- 8th Grade Math: Measuring Perimeter & Area
- 8th Grade Math: Data & Graphs
- 8th Grade Math: Probability
- 8th Grade Math: Statistics
- 8th Grade Math: Rates, Ratios & Proportions
- 8th Grade Math: Consumer Math
- 8th Grade Math: Number Sequences
- 8th Grade Math: Sets & Subsets
- 8th Grade Math: Algebraic Monomials & Polynomials