# Ch 24: Geometry for Algebra Students

### About This Chapter

## Geometry for Algebra Students - Chapter Summary

For your Regents Algebra test preparation, this chapter offers valuable instruction on basic geometric concepts that can be beneficial to algebra students, such as angles, points, lines and properties of shapes. All of the following topics are included for your study:

- Types of angles and lines
- Properties of various basic shapes
- Practice and application of the Pythagorean Theorem
- Three-dimensional figures
- Area and volume of various shapes and the application of scale factors

Each lesson offers an engaging video, a full text transcript of the video and a multiple-choice quiz. Video tags are available to help you locate specific portions on videos for additional review. Some lessons also provide links to extra lessons about basic terms and topics related to the chapter.

### Regents Mathematics Algebra I Exam Objectives

As New York State transitions to the Common Core Learning Standards, the Integrated Algebra Exam becomes the Algebra I test. All high school students in the state must pass five subject-area tests, with scores of 65 or better, to earn the Regents Diploma.

This algebra test is composed of four parts, including concepts related to number and quantity, algebra, statistics and probability and functions. The questions are multiple-choice and free response, and you'll have three hours to complete the exam. Our short, multiple-choice quizzes can provide excellent practice for test day.

### 1. Points, Lines & Angles in Geometry

Geometry is a sector of mathematics that analyzes shapes, lines, and surfaces. Explore the definitions and examples of the basics of geometry: points, lines, and angles.

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

Understanding angles and angle relationships allows for easier calculation of angle measurement. Learn how to define various types of angles, including vertical, corresponding, alternate interior angles, and how to calculate degree measurement using angle relationships.

### 3. Parallel, Perpendicular and Transverse Lines

Lines have a specific shape, but there are different types of them according to how they relate to other lines in the same plane. Learn about the different types of lines, including parallel, perpendicular, and transverse lines, and see the formulas you can use to determine the type of line.

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

Different objects come in different shapes that help achieve their purpose. Learn about the properties of different shapes, including rectangles, squares, and rhombuses.

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

There are many different properties of shapes, but the perimeter of all of them is the sum of all its sides. Explore the properties of the more complicated shapes, including quadrilaterals, parallelograms, trapezoids, and polygons.

### 6. Properties of Shapes: Triangles

Triangles are three-sided shapes with three angles. Learn the basic properties of triangles, explore the types identified by their sides and angles and types classified by angles alone, and understand different combinations for naming triangles.

### 7. Properties of Shapes: Circles

In geometry, a circle is the round shape formed by the infinite set of points an equal distance from the center. Learn the definition of a circle, and explore its various parts and properties, including the radius, diameter, circumference, pi, and chord.

### 8. Perimeter of Triangles and Rectangles

Perimeter is defined as the combined distance around a shape, object, or figure, while the perimeter of any polygon can be determined by adding the length of all sides. Learn about perimeter, how to use mathematical formulas to calculate the perimeter of triangles and rectangles, and how to use perimeter to determine the length of unknown polygon sides.

### 9. Area of Triangles and Rectangles

The area of a two-dimensional shape represents the space covered within its perimeter, but area calculations change depending on the shape. Learn how to calculate and solve the areas of right triangles, oblique triangles, and rectangles.

### 10. Circles: Area and Circumference

Like all geometric shapes, circles take up space and a formula is required to calculate the area. Learn about the area and circumference of circles, explore the formula to calculate a circle's area, and review examples that use the diameter and others that use the circumference to find the area of a circle.

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

Discover how the Pythagorean theorem helps people to solve for all sides of a triangle. Learn about the basics, purpose, and applications of the Pythagorean theorem.

### 12. 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.

### 13. Applications of Similar Triangles

Similar triangles have the same shape but differ in size. Learn about the applications of similar triangles, including how to use them and how to solve real-world problems with similar triangles.

### 14. Angles and Triangles: Practice Problems

When solving angles, they should be equal to each other or added together to equal 180, and with solving triangles, all angles in every triangle added together must equal 180 degrees. Engage in practice problems solving angles and triangles.

### 15. Vertical Angles & Complementary Angles: Definition & Examples

Vertical angles and complementary angles can be used to calculate unknown angle measurements. Learn the definition of vertical angles and review examples of how to use the properties of vertical angles and complementary angles to find the missing angle's measurements.

### 16. Overview of Three-dimensional Shapes in Geometry

Unlike two-dimensional shapes, three-dimensional shapes include a length, width, and height that give it depth. Explore the geometry of rectangular prisms, cubes, cylinders, spheres, and learn how to recognize examples of 3-D shapes in everyday objects.

### 17. How to Calculate the Volumes of Basic Shapes

The basic formula for volume is length * width * height and is necessary in geometry and the science of understanding mass in the form of basic shapes. Learn more about how to calculate the volumes of basic shapes and use the methodologies.

### 18. Volume of Cylinders, Cones, and Spheres

Volume is the capacity of an object or how much space something occupies in that object. Learn how to identify the volume formulas for cylinders, cones, and spheres, and discover why different shapes have different volumes that can be applied in real-world situations to calculate volume.

### 19. Volume of Prisms and Pyramids

The volume of prisms and pyramids can be calculated by multiplying the base and height and dividing the result by three. Learn more about the types of prisms and pyramids and how to calculate the volume of both.

### 20. 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.

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### Other Chapters

Other chapters within the NY Regents Exam - Integrated Algebra: Test Prep & Practice course

- Number Theory & Basic Arithmetic
- Problems with Decimals and Fractions
- Problems with Percents
- Problems with Exponents
- Problems with Exponential Expressions
- Problems with Radical Expressions & Equations
- Problems with Algebraic Expressions and Equations
- Distributing Terms in Algebra
- Algebraic Linear Equations & Inequalities
- Understanding Matrices & Absolute Value
- Overview of Functions
- Factoring with Variables
- Quadratics & Polynomials
- Rational Expressions & Practice
- Graphing Functions
- Calculations with Ratios, Percent & Proportions
- Understanding Sets
- Understanding Probability & Statistics
- Factorials & the Binomial Theorem
- Working with Data
- Well-Known Equations
- Intro to Trigonometry
- Measurement for Algebra Students
- About the NY Regents Examinations
- NY Regents Exam - Integrated Algebra Flashcards