Are you prepping for the Geometry Regents exam? Trying to figure out what to know cold or how to create your own cheat sheet?
We’ve researched released exams to create this ultimate guide of study tips and things to remember for the Geometry Regents. Use this guide in conjunction with our Ultimate Geometry Regents Review Guide and our 30-Day Study Plan and you’ll have everything you need to ace the test.
What We Review
The Top 5 Most Common Topics on the Geometry Regents Exam
While each Regents Geometry exam has different questions, there are trends in what topics are most often assessed. Are you curious about the specific topics you should review and practice the most before test day?
We’ve got you covered!
We tracked hundreds of official questions from the most recent Geometry Regents exams and found the patterns in what specific topics are often assessed. Below are the five most commonly-assessed topics on the Geometry Regents exam:
#1 Most Common Topic: Prove Parallelogram Theorems
Description: Prove a wide range of theorems related to parallelograms.
Frequency: This topic has been assessed in 100% of recent exams.
Pro Tip: This topic is almost always assessed as a multiple-choice question in Part I of the exam.
Math Standard: HS.G.CO.11 // Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.
Example:
Source: Regents Geometry Exam, August 2019, Question #7
#2 Most Common Topic: Congruence and Similarity of Triangles
Description: Use congruence and similarity criteria for triangles to solve problems.
Frequency: This topic has been assessed in 100% of recent exams.
Pro Tip: This topic is most often assessed as a multiple-choice question in Part I of the exam but occasionally appears as a constructed-response question.
Math Standard: HS.G.SRT.5 // Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
Example:
Source: Regents Geometry Exam, August 2019, Question #18
#3 Most Common Topic: Right Triangles in Application Problems
Description: Solve real-world application problems involving triangles using trigonometric ratios and the Pythagorean Theorem.
Frequency: This topic has been assessed in 100% of recent exams.
Pro Tip: This topic is assessed both as a multiple-choice question and as a constructed-response question on Regents Geometry exams.
Math Standard: HS.G.SRT.8 // Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
Example:
Source: Regents Geometry Exam, August 2019, Question #26
#4 Most Common Topic: Prove Theorems About Triangles
Description: Prove a wide range of theorems related to triangles.
Frequency: This topic has been assessed in 100% of recent exams.
Pro Tip: This topic is frequently assessed as a multiple-choice question but can also appear as a constructed-response question on Regents Geometry exams.
Math Standard: HS.G.CO.10 // Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.
Example:
Source: Regents Geometry Exam, August 2019, Question #5
#5 Most Common Topic: Dilations
Description: Understand dilations of a line or line segment.
Frequency: This topic has been assessed in 100% of recent exams.
Pro Tip: This topic is frequently assessed as a multiple-choice question in Part I of the Regents Geometry exam.
Math Standard: HS.G.SRT.1 // Verify experimentally the properties of dilations given by a center and a scale factor. a) A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged. b) The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
Example:
Source: Regents Geometry Exam, August 2019, Question #10
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Key Geometry Regents Question Vocabulary Cheat Sheet
Perhaps more so than any other mathematics exam, the Geometry Regents requires students to recognize and understand a variety of vocabulary terms and mathematical symbols. Memorizing all of these words and symbols can get confusing, so we’ve studied released Regents exams to create a cheat sheet for the most important Geometry terms.
Take time to review this section and commit each vocabulary term to memory. It might help you to create a deck of flashcards to practice these terms each day.
1. If your prompt says SIMILAR, think same angles, different size.
We all know what “similar” means in everyday English, but this term takes on a whole new meaning in the context of the Geometry Regents exam. When two shapes are similar, it means they have congruent angles but different side lengths.
Symbol Spotlight: Remember that the \cong symbol means congruent and \sim means similar. Congruent shapes, angles, and measurements are exactly the same, while similar shapes are proportional to one another.
It also helps to remember that when a figure is dilated, it creates a figure similar to the original. That means that it will have congruent angles, but a different size.
Example question:
Source: Regents Geometry Exam, January 2020, Question #3
2. If your prompt says RIGID MOTIONS, think about types of transformations.
You’ll likely encounter a problem that asks about rigid motions on the Geometry Regents exam. Fortunately, this term defines itself! “Rigid” tells us that the figure will maintain its size and shape, and “motion” tells us that the figure will move to a different position or direction.
There are three types of rigid motions you’ll need to remember:
- Reflections refer to a figure being flipped over a given line of reflection.
- Rotations refer to a figure being rotated a given number of degrees around a center of rotation.
- Translations refer to a figure shifting in a given direction.
Rigid motions create figures that are congruent to one another. Note that a dilation does not count as a rigid motion because it creates figures that are different sizes and thus similar, not congruent.
Example question:
Source: Regents Geometry Exam, August 2019, Question #9
3. If your prompt says ALTITUDE, think about a perpendicular line.
“Altitude” is another word that means something different in day-to-day conversations and on the Geometry Regents exam. The altitude of a triangle is a line drawn from a vertex to the opposite side such that it is perpendicular to a line containing the opposite side.
Symbol Spotlight: The symbol \perp means perpendicular. The altitude of a triangle is perpendicular to the line containing the opposite base of that triangle, which means it creates 90^\circ angles.
A couple things to remember about altitudes:
- An altitude to the base of an isosceles triangle bisects both the vertex angle and the length of the base.
- An altitude to the hypotenuse of a right triangle creates two triangles that are both similar to one another and to the original right triangle.
Example question:
Source: Regents Geometry Exam, January 2019, Question #10
4. If your prompt says PARALLELOGRAM, think about some special properties.
The definition of a parallelogram is simple enough: a quadrilateral with two pairs of parallel sides. Examples of parallelograms include squares, rectangles, and rhombuses.
For the Geometry Regents exam, you’ll also need to remember certain properties of parallelograms:
- Both pairs of opposite sides and opposite angles are congruent.
- The diagonals bisect one another.
- Each diagonal breaks the parallelogram into two congruent triangles.
Example question:
Source: Regents Geometry Exam, June 2019, Question #12
5. If your prompt says VOLUME, use your formula sheet.
We can almost guarantee that your Geometry Regents exam will include a question involving the volume of a three-dimensional figure. Lucky for you, your Regents Mathematics Reference Sheet includes the formulas for the volumes of all the shapes you might encounter.
For practice calculating the volume of three-dimensional figures, check out our guide to the Regents formula sheet. We’ve outlined how to work through different volume questions and linked to practice problems where you can try out the formulas in action.
Example question:
Source: Regents Geometry Exam, August 2018, Question #19
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3 Strategies and Tips for Multiple Choice Questions on Geometry Regents Exams
1. Practice with the Regents reference sheet before exam day
All Regents math exams use the same reference sheet, but the Geometry exam is where the reference sheet is by far the most helpful.
Download an official copy of the Regents math reference sheet.
Do not wait until the day of the exam to get familiar with what is (and is not) included on the Regents math reference sheet. You should print out a copy and start using it to solve problems while you study for the exam.
The reference sheet provides many different geometry formulas – making it really valuable for you during the exam. For a deep dive into each formula (and sample problems from actual Regents questions), read our detailed guide on the Regents reference sheet.
Tip: If there is anything you have memorized before the exam that is not included on the reference sheet, write it down on the reference sheet as soon as the exam starts. This will make sure you don’t forget it later on in the exam!
2. Use the process of elimination
Whenever you’re presented with a wide range of answer options, it can be helpful to eliminate any answer choices that you know cannot be correct. This is called the “process of elimination”.
For the Geometry Regents exam, you’ll be given 4 possible answer choices on all multiple-choice questions. It’s very likely you can eliminate at least one – and maybe even two – of the answer choices pretty easily. As you go through each possible answer choice, literally draw a line through any answer choice that must be wrong.
If you can’t decide on a final answer, take an educated guess or try a new strategy. Whatever you do: do NOT leave any question blank on your Regents exam. You do not lose credits for a wrong answer, so it’s much better to just guess instead of leaving something blank.
What makes the process of elimination such a great trick?
You originally start with a 25% chance of randomly guessing the right answer (1 out of 4). If you can eliminate two of the answer choices, that means you’ve doubled your chances of getting the question correct to 50% (1 out of 2) – awesome!
3. Don’t get “stuck” on a single problem
Most students have plenty of time to finish all the questions on the Geometry Regents exam. In fact, most students finish with many minutes leftover on the 3-hour time limit!
However, this doesn’t mean you should stay “stuck” on a single multiple-choice question as you work through the exam. It’s important to stay confident and focus on the questions you DO know really well. You can always go back to tricky questions and spend extra time thinking through different options. In fact, we often think of new ideas on how to solve tricky problems just by working on other problems elsewhere on the exam!
We generally suggest about 3 minutes for each multiple-choice question. For more details on how to pace yourself on the exam, check out our full Geometry Regents Review Guide.
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3 Strategies and Tips for Constructed Response Questions on Geometry Regents Exams
1. Know your proofs
Every Regents exam will contain free-response questions on writing proofs. This can be a challenging topic for many students. It is critical to be confident in your “proofing” skills (especially if you want a top score), so be sure you spend lots of time practicing this skill.
If you want more resources on practice with proofs, checkout our detailed Geometry Regents 30-Day Study Plan – including videos and practice resources for proofs.
2. Start with your strengths
Some students like to read all the constructed response prompts on their Regents exam before actually writing down answers. When you begin Part II of the Geometry exam (the first section that includes constructed response questions), you can quickly skim all of the questions. This might be helpful as you can find the questions you are most confident in and knock them out first.
You’ll feel motivated as you begin the constructed response questions. Pre-scanning the questions will allow you extra time for the questions that will take you longer to solve. If you decide to answer questions in your own order for the exam, just be sure you answer all the questions provided.
Remember: You should never leave a constructed response question with a blank answer.
3. Don’t get lazy (show your work)
One of the best parts of constructed response questions is that you can earn partial credit for questions even if your final answer isn’t totally correct!
To earn partial credit, it’s imperative that you show as much work as possible on every question. This means you should always write down anything you think might be relevant to solving the problem. The more accurate work you demonstrate on your test booklet, the more likely it is the exam grader will be able to award you credits.
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Geometry Regents Graphing Calculator Tips and Tricks
According to the official Regents administration directions, students will have access to a graphing calculator for the duration for the Geometry Regents exam. That means it’s time for you to get comfortable using the different functions your graphing calculator has to offer.
We’ve crafted a list of graphing calculator tips and tricks to show you how to make the most of your calculator during the Geometry Regents exam. Take some time getting familiar with these functions before the exam so that you show up on test day ready to go!
Before you dive into this Geometry-specific list, take some time to review our Algebra 1 Regents Calculator Tips and Tricks and Algebra 2 Regents Calculator Tips and Tricks.
1. Get comfortable with trigonometric functions.
In the Geometry Regents exam, you’ll be expected to recognize, understand, and apply trigonometric functions.
There are three trigonometric functions you should commit to memory: sine, cosine, and tangent. Students are often taught to remember these functions with the mnemonic Sohcahtoa. To refresh your memory, the functions are:
- The sine of an angle is the ratio of the opposite side to the hypotenuse.
- The cosine of an angle is the ratio of the adjacent side to the hypotenuse.
- The tangent of an angle is the ratio of the opposite side to the adjacent side.
Once you’ve figured out which function to use, your calculator can do the rest. Hit MODE to make sure your calculator is in “DEGREES”, and then use the appropriate trigonometric function button to solve your problem.
| Regents Question | Calculator Tip (Click to Expand) |
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2. Double check radical expressions with the click of a button.
We can guarantee that you’ll be dealing with a radical expression at some point during the Geometry Regents exam. One way that radical expressions frequently come up is in the distance formula for finding the distance between two points:
d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}
When using this formula, don’t let a math mistake bring you to the wrong answer. Instead, substitute all values into your calculator to get a decimal answer. Then, check the decimal values of the answer choices to see which is equivalent.
| Regents Question | Calculator Tip (Click to Expand) |
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3. Don’t forget about your pi key.
You’ll notice that the pi symbol (\pi) appears multiple times in the Regents mathematics reference sheet. For context, \pi is a mathematical constant that has an infinite number of digits.
However, you don’t need to spend any time memorizing the digits of pi. Instead, use the pi key on your graphing calculator in formulas and calculations. On most calculators, you can access the pi key by hitting 2ND followed by the ^ key.
With the help of this key, you can input entire formulas into your graphing calculator and avoid opportunities for miscalculations and human error.
| Regents Question | Calculator Tip (Click to Expand) |
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Summary: Things to Remember for the Geometry Regents
You’ll be surprised what a difference our study tips can make when it comes to taking the Geometry Regents exam. Some key takeaways and things to remember include:
- Make sure you know how to answer the most commonly asked questions. We can absolutely guarantee that certain topics will show up on the exam, so do yourself a favor and master these skills and concepts. Checkout our 30-day study guide for more details.
- Memorize key Geometry vocabulary. Let’s face it: math uses a lot of terms and phrases that we aren’t used to hearing in everyday life. Take the time to memorize some key terms and phrases from our Geometry cheat sheet above to set yourself up for success on the exam.
- Let your calculator become your first best friend. You can save yourself time and improve your Regents score by putting your graphing calculator to work. Spend time learning and practicing our calculator tips and tricks to maximize your Regents score.
- Let the Regents reference sheet become your second best friend. To do well on this exam, you must become familiar and confident using the Regents reference sheet. Geometry is filled with dozens of important formulas and relationships – so be sure you know exactly what is and is not included on the reference sheet. Use this post to get a more detailed analysis of the reference sheet.
We know you’ve got what it takes to pass the Geometry Regents exam! For more information on boosting your score, check out our Geometry Regents review guide.
What are Helpful Practice Resources for Geometry Regents?
Albert has a number of Geometry Regents practice tests for your test prep!
Unique from other Regents prep sites, Albert not only provides access to some of the previously released Regents tests, but also includes original New York Geometry Regents practice questions. Create your free account today.
Start your Regents test prep here
For more information on the Geometry Regents exam, check out Albert’s Geometry Regents Study Tips or our 30-day Geometry Regents Study Guide.
