# Ch 32: SAT Math: Geometry and Measurement

### About This Chapter

## SAT Math: Geometry and Measurement - Chapter Summary

This portion of the math SAT covers a wide variety of concepts. Watch our short video lessons to review the following topics:

- Types of angles and lines
- Perimeter and area of triangles and rectangles
- Area and circumference of circles
- Properties of shapes
- Similar triangles
- Pythagorean Theorem
- Volumes of basic shapes
- Properties of 3-D objects
- Parts and applications of graphs
- Transformations
- Visualizing geometry problems

In this chapter, you'll work with the graphing formulas for distance and midpoint, in addition to the point-slope formula for finding the equation of a line. You'll also explore the graphing topics of undefined slope, zero slope, absolute value, dilation, reflections, center and radius. After working your way through each lesson, take the quick quiz to make sure that you're staying on target.

### SAT Math Objectives

Your SAT math section will have 58 questions. Your test booklet will contain the formulas needed to complete the questions. The geometry and measurement portion composes 25%-30% of the test questions. You'll be asked to demonstrate your understanding of the following concepts:

- Geometric visualization
- Circles: area and circumference
- Polygons: area and perimeter
- Volume: boxes, cubes and cylinders
- Slope
- Transformations
- Similarity
- Coordinate geometry
- Properties of parallel and perpendicular lines
- Pythagorean Theorem
- Special properties of equilateral, isosceles and right triangles

Our lessons assist your review of these tested objectives and provide practice problems for working with angles and triangles, in addition to applying the Pythagorean Theorem. You'll want to use a calculator on some of the problems, so make sure that you've checked the list of approved models on the SAT student site. Unanswered questions and incorrect choices don't count against you.

### 1. 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.

### 2. 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.

### 3. Area of Triangles and Rectangles

How do you find out the area of rectangles and triangles? Learn how in this lesson! We'll look at the formulas, then practice solving problems for each shape.

### 4. Finding the Properties of Three-Dimensional Objects on the SAT

Struggling with 3-D geometry problems on the SAT, like the problems about cubes and spheres? In this lesson, you'll learn how to crack them by breaking them down into more familiar 2-D shapes and solving from there.

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

Squares pegs = square holes. Triangular pegs = triangular holes. But where does a sphere go? In this lesson, review volumes of common shapes while contrasting a sphere and a cylinder - after all, they both go into the circular hole... right?

### 6. Properties of Shapes: Circles

Circles are fundamental to everything we do. But, did you know they're much more than just round shapes? In this lesson, we'll look at the various parts of circles and how they all relate.

### 7. Circles: Area and Circumference

Understanding how to calculate the area and circumference of circles plays a vital role in some of our everyday functions. They serve as the foundation for operating with three-dimensional figures. Learn more about the area and circumference of circles in this lesson.

### 8. Graphing Circles: Identifying the Formula, Center and Radius

Discover how to graph circles by finding key information like the center and radius. Identify circles by simply looking at the formula, and vice versa.

### 9. Converting Between Radians and Degrees

Angles can be measured in degrees or radians. This lesson will explore the difference and provide you with a simple calculation that can be used to convert degrees into radians and radians into degrees.

### 10. How to Find the Arc Length of a Function

You don't always walk in a straight line. Sometimes, you want to know the distance between two points when the path is curved. In this lesson, you'll learn about finding the length of a curve.

### 11. Measurements of Lengths Involving Tangents, Chords and Secants

The lengths of chords, tangents and secants take on unique relationships when they're drawn on circles. In this lesson, we'll define those relationships and see them in action.

### 12. Finding the Area of a Sector: Formula & Practice Problems

In this lesson, you'll review your knowledge of circle vocabulary and then discover how to calculate the area of a sector of a circle. The lesson covers finding the area of the sector using degrees and radians.

### 13. How to Find the Measure of an Inscribed Angle

Finding the measure of an inscribed angle requires knowing a little information. In this lesson, we'll find the measure of an inscribed angle when we know the measure of the central angle or one or more of the arcs formed by the angle.

### 14. 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.

### 15. 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.

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### Other Chapters

Other chapters within the SAT Prep: Practice & Study Guide course

- SAT: About the Test
- SAT Writing: About the Writing Section
- SAT Writing: Text & Argument Analysis
- SAT Writing: Word Choice & Expression
- SAT Writing: Standard English Grammar
- SAT Writing: Writing & Language Test Practice
- SAT Writing: The Essay Portion
- SAT Writing: Planning and Writing Your Essay
- SAT Writing: Parts of an Essay
- SAT Writing: Sentence Clarity and Structure
- SAT Writing: Essay Writing Skills
- SAT Writing: How to Write An Argument
- SAT Writing: Supporting Your Writing
- SAT Writing: Revising Your Writing
- SAT Reading: About the Reading Section
- SAT Reading: Reading Passages
- SAT Reading: Understanding Reading Passages
- SAT Reading: Interpreting & Analyzing Text
- SAT Reading: Literary Terms
- SAT Reading: US Documents & Speeches
- SAT Vocabulary Practice
- SAT Math: About the Math Section
- SAT Math: Numbers and Operations
- SAT Math: Exponents
- SAT Math: Equations and Expressions
- SAT Math: Rational Equations and Expressions
- SAT Math: Inequalities
- SAT Math: Functions
- SAT Math: Quadratic Equations
- SAT Math: Ratios, Rates & Proportional Relationships
- SAT Math: Unit Rate & Measurement Conversions
- SAT Math: Triangles & Trigonometric Ratios
- SAT Math: Data Analysis, Statistics and Probability
- SAT Prep Flashcards
- SAT Flashcards