Very Few People Can Pass This Geometry Test. Can You?
- by Dylan Brown
- – on
- in Mind Twisters
Geometry is a subcategory of mathematics that deals with the definition and measurement of shapes, their angles, and the way in which they interact with each other. These interactions can be things like how inverse angles provide information of other angle measurements on a plane.
Most of us took a geometry class at some point in high school, or maybe even began studying the subject before that. For most, the class would usually come off as a bizarre study of shapes and concepts that didn't really make sense right off the bat, but we didn't want to ask a clarifying question and look stupid in front of the whole class. We all remember thinking, "how is this gonna be used in real life?" Well here we are, with a real life geometry quiz made just for you!
Gathered below are a wide range of geometry questions, from things like finding the value of "X" to knowing important historical mathematicians. Now we aren't going to force you to show your work, but you might want to have a pencil and some scratch paper handy!
What was your final score? Be sure to post a comment below and say what you thought the hardest question was. Did we leave out your favorite geometry question? If so, let us know what it is in the comments section!
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Are these two lines parallel or perpendicular?
Parallel and perpendicular lines are two ways of categorizing the layout of lines on a plane. They deal with whether or not lines on a plane intersect and in what way they do so. Just by looking at the image it is clear that the lines do not appear to intersect and since there are arrows on each end, it is safe to assume that the lines never will intersect. With that in mind, are these lines parallel or perpendicular?
How many sides are there on a cube?
A cube is one of many complex, three dimensional shapes that the entry level geometry student will learn about. On a two dimensional plane, there only exists a X and Y axis but to incorporate a third dimension, a new Z axis must be introduced. In this question, you are tasked with finding out how many sides there are to a cube. Hint: Start by finding at least one square on the cube, at each corner will be the start of two other squares. Use this until you can find the total number of sides.
Find the length of line "c"
Once again, you will be tasked with finding the length of a line using the pythagorean theorem. Given the image, you can see that you will have to add an extra step in order to solve this problem. You can decipher that the middle line between the triangle is a right angle which can then be used to calculate one half of the length of line c. From there, it is up to you to figure out the rest of the problem. Round to the first decimal point.
What type of angle is this?
There are three main types of angles in geometry that are commonly used to identify the wide array of angles present in shapes like triangles, rectangles, pentagons and so forth. The three main ways to identify angles are called acute angles, right angles, and obtuse angles. With that information, take a look at the photo and see what you can decipher. Hint: The angle appears to be less than 90 degrees since you can not place a square on the angle and have it fit like on a right angle.
What is the volume of this prism?
The first thing that you need to do in order to solve this question is begin by looking at the information we have. Sometimes, knowing what you don't know is important. You can isolate just the trapezoid in the foreground and use its parallel sides to get the measurement of the entire quadrilateral. From there you can apply the lengths and widths of the rest of the prism to come to the eventual answer. Round up to the first decimal place.
What type of angle is this?
There are three main types of angles in geometry that are commonly used to identify the wide array of angles present in shapes like triangles, rectangles, pentagons and so forth. The three main ways to identify angles are called acute angles, right angles, and obtuse angles. With that information, take a look at the photo and see what you can decipher. Hint: The angle appears to be more than 90 degrees since you can place a square on the angle and have it fit like on a right angle.
What is the volume of this cylinder?
Much like the triangle, the cylinder is one of the first of many complex shapes studied in geometry. From a flat perspective, you can find the measurement of the radius of the circle, square that, and then multiply it by both Pi and the height of the cylinder to be able to find the volume of the shape. So remember: find the radius and then use the rest of the information available to solve the volume of the cylinder above!
91° would be considered what type of angle?
For this question in particular, I'm not going to give you an image to go off of but will instead just give you the angle measurement and ask you to identify it. It is up to you to picture it and then determine whether or not it represents an acute angle, a right angle, and obtuse angle, or perhaps even none of the above angles. Hint: A 90° angle is a very specific type of angle that will help you on this problem.
What is the area of this triangle?
Width- 4 cm Height- 6 cm Finding the area of a triangle is similar to finding volume or perimeter on similar shapes. the formula for doing so involves taking the information of the width and height as well as using a .5 at somewhere in the equation. It is worth noting that this triangle in particular has a right angle so it is possible to determine the hypotenuse of the triangle with just the information in the image as well!
Which letter represents the vertex?
A vertex is an important point for an angle as it represents a very specific area on the line. Based on the available letters on the line, determine which one represents the vertex. All three of the points lay on the line itself so they are indeed part of the line. Here's a hint that might be able to clear some confusion for you. The vertex of an angle can lay in two possible positions. It can be the apex or the valley of a line depending on the line's orientation.
What is the angle measurement for a flat line?
A flat line is one of the simplest lines that can be drawn as it is nothing more than a connection between two points. In fact the only way this could be simpler would be if there was only a single point on the plane. With this in mind, determine what the angle measurement for a flat line would be. Hint: A flat line has a direct correlation with a right angle that lines up perfectly halfway between the line and the right angle.
Two complementary angles will add up to what degree?
Complementary and supplementary angles are two specific subcategories of angle classification that can be used to determine unknown angle measurements. For example, if someone knows that two angles are complimentary and the measurement of at least one of the two angles, they can subtract that angle from the total to determine the angle measurement of the unknown angle. Do you have what it takes to know what complementary angles will add up to? Hint- Only 90's kids will remember this one
Find the value of angle X
A-39 Degrees B- X Degrees C- 55 Degrees With the given information, you should be able to determine the value of angle X. Keep in mind that the shape is a triangle and will add up to a specific degree amount in order to maintain its status as a triangle. In this case in particular, you do not need to concern yourself with the line measurements or anything other than the angles provided. Hint: By adding the two angles and then subtracting that from the total, you can find angle X
What are the first five digits of Pi?
Excerpt from Wikipedia about Pi: "Being an irrational number, π cannot be expressed exactly as a fraction (equivalently, its decimal representation never ends and never settles into a permanent repeating pattern). Still, fractions such as 22/7 and other rational numbers are commonly used to approximate π. The digits appear to be randomly distributed. In particular, the digit sequence of π is conjectured to satisfy a specific kind of statistical randomness, but to date no proof of this has been discovered."
Find the volume of this cone
A cone is one more in the long list of introductory three dimensional shapes that will be studied in your typical geometry course. It combines elements of the pyramid and sphere together to get a pointy surface supported by a flat and circular base. Given the hypotenuse and one side of the triangle, solve for the height of the cone which you can then plug into the equation for finding a cone's volume to get the answer. Round to the first decimal place. Hint: The formula is Pi x Radius^2 x h/3
What is a bisector?
In the mathematical world, bisectors do exactly what they sound like they should do. They intersect a line at a certain point, but what they do to the intersected line is up for you to decide. Do they turn a line into an acute and obtuse angle? Perhaps it separates the intersected line into equal and congruent parts? Or maybe it gets really crazy and adds a brand new dimension to the plane! Or maybe it does none of these things! You decide.
What is special about vertical angles?
Now this image may look like the green semicircles are highlighting horizontal angles, but those are in fact examples of vertical angles. The complex relationship between two intersecting lines creates these vertical angle measurements but it is up to you to determine why they are so special and what exactly it is that makes them vertical angles. Is it the fact that the angle itself makes a V shape? Or that the measurements of the angle are equal? Or perhaps that when rotated, the angles become vertical angles.
How many degrees are there in a circle?
Coming back to the circle, we are at another complex crossroads on the path to completing this quiz. But don't worry, the end is in sight! Now when most angles are measured, there is a defined point upon which the measurement is taken which is then given a degree value. Now the circle has no real defined point to get that sort of measurement from since it is smooth, so what can you do to determine the angle measurement of an entire circle?
what is the perimeter of this pentagon?
Given that one side of the pentagon is equal to 10 meters, what is the perimeter of this pentagon? A pentagon is a five sided figure and also the name of a large government office building in the United States of America. The office building is designed to match the same shape design as the image in this picture. Hint: In this pentagon, all of the sides of the shape are equilateral, meaning that each side has the same length as the others!
What is the definition of an isosceles triangle?
Triangles are shapes that have three sides and three angles that are connected. The triangle is one of the first shapes we learn about as children, along with squares and circles, since those are the easiest shapes to understand conceptually. However, the more you begin to study the triangle, the more intricate and complex it becomes. You can start to see the many different implications of triangular geometry in everyday life, from pyramids to being used as a pivot point.
Find the value of "a"
Using the pythagorean theorem, find the value of line a. Given the information that one angle of the triangle is a right, 90 degree angle, you can use the pythagorean theorem to solve this equation. Break out your non-programmable calculators and start plugging numbers in until you get your answer! As long as you have at least two of the side measurements or a combination of side measurement and accurate angle readings, it is possible to solve the other sides of the triangle. Round up to the first decimal place.
How many sides are there to a pyramid?
A pyramid is another shape that entry level geometry students learn about. The pyramid has literal real world implications: most notably in Egypt where pharaohs and other important Egyptian royalty were buried. These tombs were designed as mazes to thwart grave robbers and serve as shrines to the gods. The pyramid does serve other functions in the mathematical world and can be used in all sorts of geometry problems. Hint: Use the same method for finding the sides of a pyramid that you did for the cube!
Two supplementary angles will add up to what degree?
Complementary and supplementary angles are two specific subcategories of angle classification that can be used to determine unknown angle measurements. For example, if someone knows that two angles are supplementary and the measurement of at least one of the two angles, they can subtract that angle from the total to determine the angle measurement of the unknown angle. Do you have what it takes to know what supplementary angles will add up to? Hint- Owls can turn their heads up to this degree and beyond!
How are the radius and diameter of a circle related?
The circle is one of the most complex yet deceptively simple looking shapes in all existence! A circle is comprised of many different points of interest and there are two in particular that I want you to think about for this particular question and that is: how are the radius and diameter of a circle related? I'll give you a hint: both the radius and diameter are elements of the circle that can be used to determine the circumference of a circle.
Find the area of this shape
This question will task you with breaking apart the shape into at least two individual shapes and finding the areas of them before combining your answers together to get the final answer. This shape is difficult to solve with just one equation because its dimensions are not common enough for it to receive a unique equation. Hint: the best way to go about solving this problem is by dividing the shape into two, easily measurable quadrilaterals and then finding their individual areas.
What is the definition of a scalene triangle?
A scalene triangle is a triangle that has not been covered on this quiz at all, but better late than never! We've been through equilateral, isosceles, and right triangles up until this point but now we tackle the hardest triangle to define right out of the gate. Do you have what it takes to get the right answer and move on to the next question? Hint: In order to define this triangle, look at the relationship between both the lines and the angles.
What formula do you use to calculate slope?
Slope is an incredibly important thing to calculate in both algebra and geometry and provides a plethora of information about the chart. A slope can be positive or negative and can change and fluctuate in value depending on the different points in the graph. Different plots relay different information. For example, a scatter plot slope will provide an accurate average and show the bias for a slope. Hint- you may be asking yourself "Y" everything in this equation is equal to some more letters.
6(2X) + 2X= 126 Find the Value of X
This problem will continue testing your skills as a mathematician and Einstein level genius. Solving for X is a technique that would have been learned in algebra but is still applicable to geometry in terms of solving different types of factors and equations. Hint: In order to solve this problem, you need to have only one x on one side of the equation. How you go about isolating it is up to you, but be sure to double check your math!
4(4x) + 2(x)=72 Find the value of x
I hope you remember your order of operations, because now is gonna be the time to use it! Solving for X is a technique that would have been learned in algebra but is still applicable to geometry in terms of solving different types of factors and equations. Hint: In order to solve this problem, you need to have only one x on one side of the equation. How you go about isolating it is up to you, but be sure to double check your math!
Find the diameter of the circle
If the circumference of the circle is equal to 8π, then what would the diameter of the circle be? I'll give you a hint to help you get started: Do you know that the equation to find the circumference of a circle is? Circumference = 2πr When you plug in the known quantities from the question, you should be left with just one unknown variable which you can then solve for by isolating it on one side of the equals sign! Good luck!
Who came up with the Pythagorean Theorem?
Excerpt from Wikipedia: "In mathematics, the Pythagorean theorem is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. The theorem can be written as an equation relating the lengths of the sides a, b and c, often called the "Pythagorean equation": a^{2}+b^{2}=c^{2},} a^{2}+b^{2}=c^{2}, where c represents the length of the hypotenuse and a and b the lengths of the triangle's other two sides."
What is the name of this formula?
This formula is defined on wikipedia as: "In elementary algebra, the formula is the solution of the -----------. There are other ways to solve the ------------- instead of using the formula, such as factoring, completing the square, or graphing. Using the -------- formula is often the most convenient way." Given that information, determine what the different letters and numbers in that sequence mean as a whole. Hint: square roots and numbers squared are the inverse of each other.
Who is The Father of Geometry?
Excerpt from Science Penguin: "a Greek mathematician, often referred to as the “Father of Geometry”. He was active in Alexandria during the reign of Ptolemy I (323–283 BC). His Elements is one of the most influential works in the history of mathematics, serving as the main textbook for teaching mathematics (especially geometry) from the time of its publication until the late 19th or early 20th century. In the Elements, he deduced the principles of what is now called Euclidean geometry from a small set of axioms. He also wrote works on perspective, conic sections, spherical geometry, number theory and rigor."
All opposite rays are...?
Excerpt from Math Open Reference on the nature of rays: "One way to think of a ray is a line with one end. A ray starts at a given point and goes off in a certain direction forever, to infinity. The point where the ray starts is called (confusingly) the endpoint. On its way to infinity it may pass through one or more other points. In the figure above, the ray starts at A and also passes through B. A ray is one-dimensional. It has zero width. If you draw a ray with a pencil, examination with a microscope would show that the pencil mark has a measurable width. The pencil line is just a way to illustrate the idea on paper. In geometry however, a ray has no width. A ray has no measurable length, because it goes on forever in one direction."
Extra Credit: What is the best quiz site on the net?
What sort of test would this be if I didn't offer up some extra credit for my hard working students? A lousy one, that's what! Thanks for taking the time out of your day to participate in this quiz, I hope you at least got a kick out of this refresher course and maybe remembered something from a class you took years ago. I would be eternally grateful if you pass this quiz along to your friends and family and share it on social media! Thanks so much!