# Ch 5: Triangles, Theorems and Proofs: Homework Help

### About This Chapter

## How it works:

- Identify which concepts are covered on your triangles, theorems and proofs homework.
- Find videos on those topics within this chapter.
- Watch fun videos, pausing and reviewing as needed.
- Complete sample problems and get instant feedback.
- Finish your triangles, theorems and proofs homework with ease!

## Topics from your homework you'll be able to complete:

- ASA, SAS and SSS postulates and congruent triangles
- Corresponding parts of congruent triangles are congruent (CPCTC)
- Converse of a statement
- Similarity transformations
- Congruence and similarity in triangles
- Hypotenuse angle (HA) and hypotenuse leg (HL) theorems
- Angle bisector theorem
- Perpendicular bisector theorem
- Congruency of isosceles and right triangles

### 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.

### 12. Mathematical Proof: Definition & Examples

Have you ever made a statement that someone challenged you to prove to be true? You have to explain things in a logical and indisputable way in order to do that. In this lesson, you'll learn different ways that statements can be proven in mathematics.

### 13. Perpendicular Slope: Definition & Examples

Review what perpendicular lines are and what the slope of a line is. Learn about the relationship between slopes of perpendicular lines through definitions and examples.

### 14. Side-Angle-Side (SAS) Triangle: Definition, Theorem & Formula

In this lesson we will learn about trigonometry and geometry. The SAS theorem ties together those two subjects into a formula which allows us to find the area of a triangle.

### 15. Square Prism: Definition & Examples

In this lesson, learn what prisms are and what makes square prisms unique. Included are a few examples of square prisms and the qualities that make up these three dimensional objects.

### 16. 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.

### 17. Two-Column Proof in Geometry: Definition & Examples

This lesson will discuss one method of writing proofs, the two-column proof. We will explore some examples and provide some guiding steps you may use to write an effective two-column proof.

### 18. What is a Vector in Math? - Definition & Examples

This lesson explores vectors, operations with vectors, and modern uses of vectors. Using relevant examples and diagrams, the lesson will demonstrate the applications of vectors in the world.

### 19. What is an Acute Angle? - Definition, Description & Examples

In this lesson, you'll learn what makes an angle acute and see a few different examples of them. After the lesson, you can test your new knowledge with a brief quiz.

### 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 High School Geometry: Homework Help Resource course

- Foundations of Geometry: Homework Help
- Logic in Mathematics: Homework Help
- Introduction to Geometric Figures: Homework Help
- Properties of Triangles: Homework Help
- Parallel Lines and Polygons: Homework Help
- Similar Polygons: Homework Help
- Quadrilaterals: Homework Help
- Circular Arcs and Circles: Homework Help
- Conic Sections: Homework Help
- Geometric Solids: Homework Help
- Analytical Geometry: Homework Help
- Introduction to Trigonometry: Homework Help