Geometry Trivia

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

From Quiz Life of Pi

Answer: March 14th

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.

From Quiz Straight Lines: The Knowledge

Answer: Shortest route through points (a) and (b)

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.

From Quiz Circle Theorems

Answer: 90 degrees

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.

From Quiz Writing a Two-Column Proof

Answer: givens.

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.

From Quiz Trigonometry I

Answer: 7pi/12

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).

From Quiz Right Triangles

Answer: side CA

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~.

From Quiz Geometry

Answer: obtuse

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

From Quiz Gee, I'm a Tree!

Answer: Rectangle

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.

From Quiz Geometry Terms

Answer: Algorithm

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.

From Quiz The Mysteries of Many-faced Mathematical Parrots

Answer: Corner

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

From Quiz Circle Theorems

Answer: Subtended

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.

From Quiz Writing a Two-Column Proof

Answer: supplemental.

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.

From Quiz Geometry Who Am I?

Answer: Right Angle

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.

From Quiz Trigonometry I

Answer: x=210 degrees, x=330 degrees

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

From Quiz Right Triangles

Answer: 45 degrees

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*.

From Quiz Geometry

Answer: 24 times the square root of 3

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.

From Quiz Considering A Room

Answer: 1200

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.

From Quiz Gee, I'm a Tree!

Answer: Icosahedron

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.

From Quiz Geometry Terms

Answer: Pentadecagon

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.

From Quiz The Mysteries of Many-faced Mathematical Parrots

Answer: Tetrahedron

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.

From Quiz Straight Lines: The Knowledge

Answer: 3

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.

From Quiz Circle Theorems

Answer: Tangent

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.

From Quiz Trigonometry I

Answer: -N& - n &negative n

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

From Quiz Right Triangles

Answer: AB^2 + BC^2 = AC^2

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*.

From Quiz Geometry

Answer: 90

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.

From Quiz Considering A Room

Answer: 680

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

From Quiz Gee, I'm a Tree!

Answer: Mobius Strip

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.

From Quiz Geometry Terms

Answer: Equidistant

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.

From Quiz The Mysteries of Many-faced Mathematical Parrots

Answer: Equilateral triangles

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.

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Last Updated Apr 22 2024 11:00 AM

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