As the title states, this quiz will examine examples of geometric shapes or concepts that we can find in our daily life, both natural and man-made.

**Easier**, 10 Qns, Gispepfu, Aug 07 23

A right triangle is nothing but a triangle which has one angle having a measure of 90 degrees. Test your knowledge about these, in a mixture of practical and theoretical questions. (Don't worry, no trigonometry involved!) **Average**, 10 Qns, achernar,
May 19 22

Finding your position in space is useful for mathematicians as well as navigators. Do you want to plot a function, draw a line or describe a solid shape? Take this quiz and exploit coordinate geometry! **Average**, 10 Qns, CellarDoor,
Nov 09 09

For each question, I will give a description of either a plane shape or a solid. You must give the MOST GENERAL shape which fits the description. **Difficult**, 10 Qns, kevinatilusa,
Dec 05 13

There are many ways of finding out the size of angles within circles. How good are you at geometry? Enjoy! **Average**, 10 Qns, jonnowales,
May 10 17

All you need to know about straight lines and then some! I hope you enjoy this geometry quiz. **Average**, 10 Qns, jonnowales,
Aug 09 22

Welcome to the show! Ten polygons will make their performances. Have fun and enjoy! **Average**, 10 Qns, Matthew_07,
Jun 05 08

If the world we see is only 3-dimensional, how can we visualize 4 (or more) dimensions? One way is by analogy. Picture versions of an object in 1, then 2, then 3 dimensions. Whatever patterns you see may give you clues about the 4th dimension. **Tough**, 10 Qns, kevinatilusa,
Aug 05 18

The German mathematician August L. Crelle found it incredible that a figure as simple as a triangle could have so many properties. **Easier**, 10 Qns, masfon,
Aug 17 19

Quick Question

From Quiz "

Take a journey with me, all about the life of Pi. Good luck and have fun! **Average**, 10 Qns, salami_swami,
Jan 08 21

If you know geometry, this will be a very easy quiz! **Average**, 5 Qns, ashalia,
Jun 19 19

Here are a list of people and objects I met during my high school geometry class. How many of them do you know? **Average**, 10 Qns, tralfaz,
Feb 12 05

This is a true-false quiz on various aspects of non-Euclidean Geometry. No problems, just conceptual questions. **Tough**, 10 Qns, redsoxfan325,
Feb 09 19

How much do you know about those (mostly regular) solid POLYhedra? **Average**, 10 Qns, Flamis,
Jul 26 10

Two-column proofs are the bane of a geometry student's existence. Draw a parallelogram and label the corners ABCD going clockwise. We are going to prove that the opposite sides are congruent. Ready to go? **Average**, 10 Qns, tralfaz,
Jan 14 18

Here is a quiz to put your knowledge of Geometry to the test! **Difficult**, 10 Qns, KKid4,
Jun 18 21

This quiz is about considering a room. Please tell me if you like this quiz. **Tough**, 10 Qns, Cardys,
Jul 29 23

The first in a series of quizzes about trigonometry. No calculators are needed on this quiz. **Difficult**, 5 Qns, Diceazed,
May 06 14

1. What day is National Pi Day in the U.S.? (Think about pi...)

Answer:

National Pi Day falls on March 14th. This is because March is the third month (3) and the 14th is day 14 (.14). Therefore, the day of March 14th can be written as "3.14", which is the number that is pi. However, National Pi Day falls on July 22 in other parts of the world, where the date is written as day/month instead of month/day, so Pi Day would be 22/7.

2. Mathematically, in terms of points (a) and (b), how could a straight line segment be defined?

Answer:

For instance, if points (a) and (b) are found on the circumference of a circle, the straight line would be a chord or, perhaps, the diameter or even a line of infinite length which passes through both points (a) and (b). The shortest route from the first point to the second point will always be in a straight line. Any longer distance would most likely be curved.

3. One of the easiest circle theorems to remember is to do with angles in a semi-circle. If two straight lines are drawn from either end of the diameter of a circle and meet at a point on the circumference, what will the angle always be?

Answer:

Two straight lines from either end of the diameter will always meet at a right angle to each other on the circumference. This applies regardless of the length of the diameter and circumference of the circle.

4. The information that is provided at the beginning of a proof is typically called the . . .

Answer:

The givens form a critical part of a proof. The appearance of a diagram is not sufficient for a proof; instead all information must be explicitly given to the reader to get started.

5. What is the supplement of 75 degrees, in radians?

Answer:

First we must convert 75 degrees to radians. To do this, me must multiply 75 by pi/180. This equals 75pi/180, which simplifies to 5pi/12. Remember that supplementary angles add up to 180 degrees, which is equal to pi in radians. So, to find the supplement of 5pi/12, we must subtract it from pi. pi-5pi/12=7pi/12 (Note: we can also find the supplement of 75 degrees in degrees, and then convert that to radians, for the answer would remain the same).

6. A right triangle ABC is given where angle B = 90 degrees.
Which side of the triangle is the longest?

Answer:

In the given triangle ABC, angle B = 90 degrees. In a right triangle, the side opposite the right angle (which in this case is angle B), is always the longest. Hence, AC is the longest side of the triangle. The longest side of a right triangle is commonly referred to as the ~hypotenuse~.

7. Assume a triangle ABC. Its legs are of lengths 2, 2, and 3. What type of triangle is it?

Answer:

2^2 + 2^2 less than 3^2, so the triangle is obtuse.

8. Which plane figure is defined as any polygon with exactly 4 angles, all of whom are equal?

Answer:

Another way of defining a rectangle is a shape where the diagonals both bisect each other and are equal. While all squares are rectangles, not all rectangles are squares.

9. What is a sequence of steps leading to a desired end?

Answer:

Ambiguous means not stable, Hierarchy means a chart that shows varying levels of importance, and Sector means part of a circle containing its center and an arc.

10. Which part of a polyhedron is called a vertex?

Answer:

If you're talking about more than one corner, they're called vertices. The word "vertex" comes from a Latin word meaning "turning point".

11. When an angle is formed from two points on the circumference and two straight lines drawn from these two points meet at another point on the same circumference, it is said that the angle is ________ by an arc.

Answer:

If an angle is subtended by an arc then the point on the circumference where the straight lines from the two points meet will have a certain angle. This can be measured with a protractor. If a second example of this happens whereby from the same two points on the circumference another meeting point is formed, then that second angle will be equal to the first angle. Angles are equal when subtended by the same arc (a=b etc). It is also possible to say that angles are equal when subtended by the same chord. The difference between a chord and an arc is, whether a straight line is drawn between the two points marked on the circumference.

12. The first thing we do is to draw a segment from B to D. Items added to a geometric diagram to help with the proof are called . . .

Answer:

To draw a line, you MUST have two points! A common mistake I see students make is to start with one point then guess where the other end should go. That turns a construction into a sketch.

13. Talk about having an identity crisis. Most people define me as an angle of 90 degrees. That's not exactly a definition though; 90 degrees is my size. My definition is "the angle formed when two lines meet such that adjacent angles are congruent".

Answer:

Another definition for a right angle is a quarter of a circle. Right angles are very important in the geometry of triangles - also known as trigonometry.

14. Find all x on [0 degrees, 360 degrees) for which csc(x)=-2.

Answer:

Since csc x=-2, sin x=-1/2. The 2 angles where this occurs is 210 degrees and 330 degrees.

15. There is a right triangle PQR where:
angle Q = 90 degrees;
angle P = angle R.
What is the measure of angles P and R?

Answer:

In the given triangle PQR, angle Q = 90 degrees. Now let us assume: angle P = angle R = x. By the angle sum property of a triangle, the sum of the three angles of a triangle is equal to 180 degrees. => angle P + angle Q + angle R = 180 degrees => x + x + 90 degrees = 180 degrees => 2x = 90 degrees => x = 45 degrees Hence, *both angle P and angle R = 45 degrees*.

16. Find the area of a regular hexagon with a side length of 4.

Answer:

First, use the theorem to find the area of a regular polygon: A = 1/2 * A * P, where A = the apothem and P = the perimeter of the figure. Since it's a hexagon, it has six sides, which are all 4 (so the perimeter is 6 * 4 = 24). Put this into the equation and you now have A = 1/2 * a * 24. You can now reduce this to A = 12 * a, or A = 12a. This is because 24 * 1/2 = 12. In hexagons, you can set up 6 equilateral triangles in its interior, with sides of 4. Divide any of these in half, and you are given a 30-60-90 triangle, whose side lengths are proportional 1:square root of 3:2, where 1 is the short leg, 2 is the hypotenuse, and the square root of 3 is the long leg. You know this is a 30-60-90 triangle because 2, the shorter leg, is half of 4, the hypotenuse. Then you can multiply the shorter leg, 2, by the square root of 3 to get 2 times the square root of 3 for the apothem. This is because of the proportion mentioned above. Now, plug this into the equation A=12*2 times the square root of 3. Your answer, after simplifying, is 24 times the square root of 3. Not too complicated.

17. With a rectangular room with measurements of a length of 10ft, width of 12ft, and height of 10ft, what would the dimensions of the room be in cubic feet?

Answer:

Like the square footage of a room, the cubic footage just takes the height into the equation, so is calculated as 10 X 12 X 10 = 1200.

18. Which Solid can be defined as the regular polyhedron (a solid with all faces identical regular polygons) with the greatest number of faces?

Answer:

An icosahedron is a shape with 20 triangular faces, 30 edges (lines where two faces meet) and 12 vertices. The icosahedron, dodecahedron, tetrahedron, octahedron, and cube are the only 5 regular polyhedra. Plato considered these the most perfect of shapes, so they are actually sometimes just referred to as the Platonic solids.

19. What is a 15-sided polygon?

Answer:

A nonagon is a nine-sided polygon, a Dodecagon is a twelve-sided polygon, and an enneagon is another name for a nine-sided polygon.

20. The simplest regular polyhedron has just four faces. What is it called?

Answer:

If you've ever played with polyhedral dice, you'll know the tetrahedron as the d4, the four-sided die (also known as the caltrop - even those who haven't played will probably wince at the thought of accidentally standing on a little pyramid made of hard plastic resin!) The caltrop is in reality a nasty little device composed of four spikes pointing outwards into the corners of a tetrahedron. This meant that when a number were tossed into the path of oncoming cavalry, each had a spike that was pointing upwards - with painful consequences.

21. By analysing the equation of a straight line which in this instance will be "y = 3x + 9", what would the gradient be?

Answer:

By using the important formula "y = mx + c" this all becomes clear. The gradient is indicated by the letter "m". In the equation given above, m = 3. Therefore, the gradient or slope of the line will be +3.

22. What is the geometric name given to a straight line which touches the circumference of a circle at one point only?

Answer:

A tangent is the name of a straight line which touches the circumference of a circle at only one point. A tangent can meet the circumference at any point around a circle.

23. If sin(53 degrees)=N, what does sin(-53 degrees)=?

Answer:

Remember that the sine function is odd, so sin(-x)=-sin(x). So sin(-53 degrees)=-sin(53 degrees)=-N.

24. The Pythagorean Theorem states that:
"The square of the hypotenuse of a right angle triangle is equal to the sum of the squares of the other two sides."
This means that, in a right triangle ABC with hypotenuse AC:

Answer:

Let me try to explain this with the help of a triangle ABC, where: AC is the hypotenuse; AB and BC are the other sides. The Pythagorean theorem states that: "The square of the hypotenuse of a right angle triangle is equal to the sum of the squares of the other two sides." >> The square of the hypotenuse... Here AC is the hypotenuse. By squaring it we get AC^2. >> ...the sum of the squares of the other two sides. The other two sides are AB and BC. If we square them we get AB^2 and BC^2. And their sum is: AB^2 + AC^2. >> ...is equal to...: With this we can conclude that *AB^2 + BC^2 = AC^2*.

25. In a transversal, you have 2 lines (AB and CD) whose slopes are 3/2 and 3/2 intersecting the transversal (EF), and the slope of the transversal is negative 2/3. Their points of intersection are G and H. What is the measure of angle AGE?

Answer:

If the slopes of the 2 intersected lines are both 3/2, then they are parallel. The slope of the transversal is -2/3, or the opposite of the reciprocal of the other lines. This means that they are both perpendicular to the transversal, and all 8 angles are 90.

26. Taking a rectangular room with measurements of a length of 10ft, width of 12ft, and height of 10ft, what is the surface area of the room in square feet?

Answer:

Surface area takes length times width plus length times height plus height times width and multiply each of these by two. 2(10 X 12) + 2(10 X 10) + 2(10 X 12) = 340

27. What shape is created by taking a rectangular sheet of paper, giving it a "twist" and gluing the two ends of the strips together?

Answer:

This shape has many interesting properties. First of all, it only has one side! If you started at a point and traced a pencil down the center of the strip until you came back where you started from, it would have actually transversed both "sides" of the strip. Furthermore, if you take a pair of scissors and cut down the center of the strip, you will be left with one piece even after supposedly cutting it in half.

28. Which term means the same distance from something?

Answer:

Equilateral means equal in length, Equianglular means having angles of the same measure, and Proportional means one of four numbers that form a true proportion.

29. What shape are the faces of a regular tetrahedron?

Answer:

Which explains why a tetrahedron is sometimes called a triangular pyramid. The tetrahedron is also seen in chemistry, in a myriad of covalent molecules, starting with CH4, methane - which has a carbon atom in the centre and four hydrogen atoms in the vertices of a regular tetrahedron.

This is category 7610

Last Updated Feb 25 2024 9:08 AM

Last Updated Feb 25 2024 9:08 AM

= added recently, = Editor's Pick = FunTrivia Editor = Gold Member

· All questions, answers, and quiz content on this website is copyright FunTrivia, Inc and may not be reproduced without permission. Any images from TV shows and movies are copyright their studios, and are being used under "fair use" for commentary and education.