# Ch 13: ELM Test - Geometry: Properties of Objects

### About This Chapter

## ELM Geometry: Perimeter, Area & Volume - Chapter Summary

Study the following concepts in geometry in preparation for the ELM math placement exam:

- Properties of Shapes: Triangles, Circles and Rectangles
- Properties of Shapes: Quadrilaterals, Parallelograms, Trapezoids, Polygons
- How to Identify Similar Triangles
- Applications of Similar Triangles
- Congruent and Similar Shapes
- Applying Scale Factors to Perimeter, Area, and Volume of Similar Figures
- Parallel, Perpendicular and Transverse Lines
- Types of Angles: Vertical, Corresponding, Alternate Interior & Others
- Angles and Triangles: Practice Problems
- The Pythagorean Theorem: Practice and Application

## ELM Objectives

The ELM is a math proficiency exam required for all incoming students to schools in the California State University system. You can learn more about the topics on the ELM by clicking here.

The lessons in this chapter are dedicated to the Properties of Objects of the Geometry section of the ELM exam. Geometry constitutes approximately 30% of the entire exam. Students can watch our online videos and test their skills with interactive quizzes.

Other topics in Geometry covered by this course include:

- Finding the perimeter of geometric shapes
- Calculating the area of geometric shapes
- Using the Pythagorean Theorem
- Identifying points on the number line
- Graphing functions with one or more variables

### 1. Properties of Shapes: Rectangles, Squares and Rhombuses

What's the difference between a square and a rectangle? What about a rhombus and a square? In this lesson, we'll look at the properties of these shapes.

### 2. Properties of Shapes: Quadrilaterals, Parallelograms, Trapezoids, Polygons

Four-sided objects are more than just squares and rectangles. In this lesson, we'll discuss quadrilaterals, parallelograms and trapezoids. We'll also discuss polygons, objects that can have more sides than you can count.

### 3. 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.

### 4. 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.

### 5. Properties of Congruent and Similar Shapes

In this lesson, we'll look at triangles, rectangles and other shapes that share properties. This includes both congruent and similar shapes. We'll also practice identifying the missing properties of these shapes.

### 6. Parallel, Perpendicular and Transverse Lines

What are the different types of lines? Where are they visible in the real world and how can you recognize them? Find out here and test your knowledge with a quiz.

### 7. Types of Angles: Vertical, Corresponding, Alternate Interior & Others

In addition to basic right, acute, or obtuse angles, there are many other types of angles or angle relationships. In this lesson, we will learn to identify these angle relationships and discuss their measurements.

### 8. Angles and Triangles: Practice Problems

Want more practice solving with angle pairs? How about more review for solving angles in triangles? Look no further. Get more practice here, and test your ability with a quiz.

### 9. The Pythagorean Theorem: Practice and Application

The Pythagorean theorem is one of the most famous geometric theorems. Written by the Greek mathematician Pythagoras, this theorem makes it possible to find a missing side length of a right triangle. Learn more about the famous theorem here and test your understanding with a quiz.

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

How do shapes change sizes yet retain their proportions and similarities to other shapes? In this lesson, we'll look at what a scale factor is and how to apply it. We'll consider scale factors with regards to three different aspects of similar shapes: perimeter, area and volume.

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### Other Chapters

Other chapters within the ELM: CSU Math Study Guide course

- ELM Test - Numbers and Data: Basic Arithmetic Calculations
- ELM Test - Numbers and Data: Rational Numbers
- ELM Test - Numbers and Data: Decimals and Percents
- ELM Test - Numbers and Data: Irrational Numbers
- ELM Test - Numbers and Data: Data & Statistics
- ELM Test - Algebra: Basic Expressions
- ELM Test - Algebra: Exponents
- ELM Test - Algebra: Linear Equations & Inequalities
- ELM Test - Algebra: Absolute Value Equations & Inequalities
- ELM Test - Algebra: Polynomials
- ELM Test - Algebra: Rational Expressions
- ELM Test - Geometry: Perimeter, Area & Volume
- ELM Test - Geometry: Graphing Basics
- ELM Test - Geometry: Graphing Functions
- About the ELM Test
- ELM Flashcards