# Ch 43: WEST Middle Grades Math: Triangle Theorems & Proofs

### About This Chapter

## WEST Middle Grades Math: Triangle Theorems & Proofs - Chapter Summary

Use these lessons to review the various theorems, postulates and proofs of triangles. In this chapter, lessons cover the following topics:

- SAS, ASA and SSS triangle congruence postulates
- The converse of a statement
- How to prove relationships using congruence and similarity
- Angle-angle-side, hypotenuse angle and hypotenuse leg theorems
- The perpendicular bisector and angle bisector theorems
- Congruency of right triangles
- Congruency of isosceles triangles

Our video lessons, taught by expert instructors, offer several features to make studying an efficient and fun process. Videos can be viewed as many times as necessary to be sure you fully grasp the materials. Use video tags to quickly jump to main ideas within the lesson. As an additional study aid, read lesson transcripts to reinforce what you've seen in the lessons.

### 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. 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.

### 6. 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.

### 7. 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.

### 8. 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.

### 9. 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.

### 10. 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.

### 11. 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.

### 12. 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.

### 13. 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.

### 14. 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 WEST Middle Grades Mathematics (203): Practice & Study Guide course

- WEST Middle Grades Math: Basic Arithmetic Operations
- WEST Middle Grades Math: Solving Math Word Problems
- WEST Middle Grades Math: Properties of Numbers
- WEST Middle Grades Math: Estimating & Rounding
- WEST Middle Grades Math: Number Theory
- WEST Middle Grades Math: Roots & Radical Expressions
- WEST Middle Grades Math: Exponents & Exponential Expressions
- WEST Middle Grades Math: Scientific Notation
- WEST Middle Grades Math: Simplifying Whole Number Expressions
- WEST Middle Grades Math: Integers
- WEST Middle Grades Math: Rational Numbers
- WEST Middle Grades Math: Introduction to Fractions
- WEST Middle Grades Math: Operations with Fractions
- WEST Middle Grades Math: Introduction to Decimals
- WEST Middle Grades Math: Operations with Decimals
- WEST Middle Grades Math: Percents
- WEST Middle Grades Math: Money & Consumer Math
- WEST Middle Grades Math: Number Patterns & Sequences
- WEST Middle Grades Math: Properties of Functions
- WEST Middle Grades Math: Graphing Functions
- WEST Middle Grades Math: Negative Numbers
- WEST Middle Grades Math: Absolute Value
- WEST Middle Grades Math: Inequalities
- WEST Middle Grades Math: Factoring
- WEST Middle Grades Math: Monomials & Polynomials
- WEST Middle Grades Math: Writing Algebraic Expressions
- WEST Middle Grades Math: Basic Algebraic Expressions
- WEST Middle Grades Math: Algebraic Distribution
- WEST Middle Grades Math: Writing & Solving One-Step Equations
- WEST Middle Grades Math: Writing & Solving Two-Step Equations
- WEST Middle Grades Math: Simplifying & Solving Rational Expressions
- WEST Middle Grades Math: The Coordinate Graph
- WEST Middle Grades Math: Linear Equations
- WEST Middle Grades Math: Systems of Linear Equations
- WEST Middle Grades Math: Rates, Ratios & Proportions
- WEST Middle Grades Math: Measurements
- WEST Middle Grades Math: Perimeter & Area
- WEST Middle Grades Math: Polyhedrons & Geometric Solids
- WEST Middle Grades Math: Symmetry, Similarity & Congruence
- WEST Middle Grades Math: Properties of Lines
- WEST Middle Grades Math: Angles
- WEST Middle Grades Math: Triangles
- WEST Middle Grades Math: Similar Polygons
- WEST Middle Grades Math: The Pythagorean Theorem
- WEST Middle Grades Math: Quadrilaterals
- WEST Middle Grades Math: Circles
- WEST Middle Grades Math: Circular Arcs & Measurement
- WEST Middle Grades Math: Transformations
- WEST Middle Grades Math: Data & Graphs
- WEST Middle Grades Math: Statistics
- WEST Middle Grades Math: Data Collection
- WEST Middle Grades Math: Samples & Populations
- WEST Middle Grades Math: Probability
- WEST Middle Grades Math: Sets
- WEST Middle Grades Mathematics Flashcards