# Ch 8: Holt Geometry Chapter 8: Similar Shapes

### About This Chapter

## How it works:

- Identify the lessons in Holt Geometry's Similar Shapes chapter with which you need help.
- Find the corresponding video lessons within this companion course chapter.
- Watch fun videos that cover the similar shape topics you need to learn or review.
- Complete the quizzes to test your understanding.
- If you need additional help, rewatch the videos until you've mastered the material or submit a question for one of our instructors.

## Students will learn:

- Definitions of similar polygons
- The triangle proportionality theorem
- The Angle-Angle-Side theorem
- The Hypotenuse-Leg theorem
- The Hypotenuse-Angle theorem
- Applications of scale factors for similar figures

*Holt Geometry is a registered trademark of Holt, Rinehart and Winston, which is not affiliated with Study.com.*

### 1. Similar Polygons: Definition and Examples

Similar polygons are two-dimensional shapes with straight sides that share the same angle measurements and only differ in size. Learn the definition and see real-world examples of similar polygons.

### 2. How to Identify Similar Triangles

Similar triangles are defined as two triangles that possess proportional corresponding sides and congruent corresponding angles. Triangle similarity theorems use angle and side comparisons to determine whether two triangles are similar. Learn about the language of similarity, triangle similarity theorems (Angle-Angle, Side-Angle-Side, & Side-Side-Side), and how to use theorems to identify similar triangles.

### 3. Triangle Proportionality Theorem

The triangle proportionality theorem explains that if a parallel line is draw to one side of a triangle and also crosses the other two sides, then the line divides the two sides proportionally. Learn the application of this theorem, including how to draw a parallel line and how to use the proportional sides in the calculation.

### 4. The AAS (Angle-Angle-Side) Theorem: Proof and Examples

The AAS Theorem asserts that when two angles and any given side are congruent between two triangles, the triangles are congruent. Explore this concept through practicing an example problem, and demonstrate the proof to find congruence.

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

The hypotenuse leg (HL) theorem states that two right triangles are congruent if the hypotenuse & one leg of a right triangle are congruent to the hypotenuse/leg of another right triangle. Learn about the definition, proof of the HL theorem through examples.

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

The hypotenuse angle or HA theorem states that if a hypotenuse and acute angle of a right triangle is identical to the angles of another right triangle, the two are congruent. Use a series of examples to learn how to prove, explain, and practice the HA theorem.

### 7. Applying Scale Factors to Perimeter, Area, and Volume of Similar Figures

A scale factor is a number that shows the relationship between the corresponding perimeter, area, and volume of similar figures. Learn about the scale factor along with examples of how it is applied to perimeter, area, and volume.

### Earning College Credit

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### Other Chapters

Other chapters within the Holt Geometry: Online Textbook Help course

- Holt Geometry Chapter 1: Exploring Geometry
- Holt Geometry Chapter 2: Reasoning in Geometry
- Holt Geometry Chapter 3: Parallels and Polygons
- Holt Geometry Chapter 4: Triangle Congruence
- Holt Geometry Chapter 5: Perimeter and Area
- Holt Geometry Chapter 6: Shapes in Space
- Holt Geometry Chapter 7: Surface Area and Volume
- Holt Geometry Chapter 9: Circles
- Holt Geometry Chapter 10: Trigonometry
- Holt Geometry Chapter 12: A Closer Look at Proof and Logic