Answer all the questions below and press submit to see how many you got right.
Boundary : The boundary of a 2-dimensional shape is the 1-dimensional shape that separates the 2-dimensional shape from the rest of the 2-dimensional space.
Circle : A circle is a two-dimensional shape. The boundary of a circle is a set of points that has the same distance (the radius) from the center of the circle.
Diameter : The diameter of a circle is the length of a line segment from the boundary of a circle through the center of the circle to the boundary on the other side of the circle.
Ellipse : An ellipse is a two-dimensional shape with a boundary that is a set of points for which the combined distance from two points is constant. Circles are special cases of ellipses. The boundary of an ellipse can also written as the set of points $\{(x,y)| \frac{x^2}{a^2}+\frac{y^2}{b^2}=1 \}$
Follow from : A second equation or inequality follows from an initial equation or inequality if all solutions of the initial equation are also solutions from the second equation or inequality. It does not necessarily have to be the case that all solutions of the second equation or inequality have to by solutions of the first inequality. For example $x^2=1$ follows from $x=1$, but $x^2=1$ is not equivalent to $x=1$ as -1 is a solution of $x^2=1$ but not a solution of $x=1.$
Point : A point is an element in a space. Shapes are made of sets of points.
Pythagorean theorem : The Pythagorean theorem states that in a right triangle the square of the hypotenuse $c^2$ equals the sum of the squares of the legs $a^2+b^2$. It can be used to calculate the length of a third side of a right triangle given the other two. It also can be used to calculate the lengths of diagonals in rectangles or cubes.
Radius : In a circle or sphere the radius is the distance between the center and the boundary.
Set : A set is a collection of objects.
Choose all statements that are true.
Addition : Addition is the mathematical operation that describes increasing a number by an amount equal to a second number. The mathematical symbol for addition is the plus sign $+.$ The term addition is also used for a generalization of this basic operation on numbers to functions, vectors and matrices.
Angle : If two line segments (or rays) both start at a common point the opening between the two line segments is called an angle. The common point is called vertex of the angle. The size of an angle is measured in degrees.
Area : The amount of unit squares that is needed to cover a 2-dimensional shape.
Center : The center of a circle is the unique point in the circle, such that all points on the boundary of the circle have a constant distance equal to the radius from that point. The center of a regular polygon is the point that has equal distance from all its corners.
Counterexample : A counterexample to a statement of the form 'all objects of type x have property y' is an object of type x that does not have property y. A counterexample to a statement shows that the statement is not true in general. For example the number 3 is a counterexample to the statement that all numbers are even.
Height : In a triangle a height (or altitude) is the shortest line segment that connects a side to its opposing corner. A height of a triangle is perpendicular to the side is started at. The three heights of a triangle intersect in a point, the so called orthocenter of the triangle. In a parallelogram the height is the shortest distance between two opposing sides. In a pyramid the height is the shortest distance between the base area and the corner of the pyramid that is not part of the base area. In a prism the height is the shortest distance between the two base faces.
Independence : Random variables $X,$ $Y$ are called independent if $P[X\in A, Y\in B]=P[X \in A]P[Y \in B].$ Independent identically distributed random variables feature prominently in the law of large numbers and the central limit theorem. Vectors $x_1,x_2\ldots, x_n$ are called linearly independent if $\lambda_1 x_1+\lambda_2 x_2+\ldots+\lambda_n x_n=0$ implies $\lambda_1=\lambda_2=\ldots=\lambda_n=0.$
Line : A line AB is a one-dimensional shape that includes the points A and B, all the points on the line segment in between A and B and all the points of the straight extension of the line segment beyond A and B. A line does not have an endpoint.
Perpendicular line : Two lines are called perpendicular if they cross in a right angle.
Right angle : A right angle is an angle equal to $90^{\circ}.$
Thales' theorem : Given a circle, points A, B and C on the circle such that the line segment AB goes through the center of the circle, the theorem of Thales says that the angle ACB is a right angle making ABC a right triangle. Thales' theorem is a special case of the inscribed circle theorem.
Theorem : A mathematical result that has been proven to hold true under the assumptions that are stated in the theorem. The most famous theorems have name like for example the Pythagorean theorem or Fermat's little theorem.
Triangle : A triangle is a polygon with three corners and three sides. You can calculate the area of a triangle by multiplying half the length of the base by the height on that base. The sum of the interior angles in a triangle is always $180^{\circ}.$
A line crosses the center of a circle and crosses the circle in points A and B. We pick any point C on the circle not equal to A or B. Choose all the statements about the triangle ABC that are true.
Adjacent : Adjacent means next to each other.
Adjacent corner : Adjacent corners in a polygon are corners that are linked by a side.
Degree : For angles one degree is defined as the angle represented by a $\frac{1}{360}$ of the angle represented by a full circle. For measuring temperatures one can use either degrees Celsius or degrees Fahrenheit. In a polynomial the degree describes the highest exponent of $x$ that has a non-zero coefficient. For example the degree of $1+x+x^2$ is 2.
Length : Length is the attribute of a one-dimensional shape that can be measured with a measuring tape.
Opposite angle : In a quadrilateral an opposite angle is the angle at the opposite corner of the corner where the angle is located.
Opposite corner : In a quadrilateral the opposite corner is the corner that does not share a side with the corner in refers to. In a polygon with an even number $2n$ of corners, the opposite corner refers to the corner you reach when moving $n$ corners away from the current corner.
Opposite side : In a quadrilateral the opposite side of a side refers to the side that does not share a corner with the original side.
Parallel : Two lines in a two-dimensional plane are called parallel if they never cross.
Parallelogram : A parallelogram is a quadrilateral with 2 pairs of parallel sides. Rectangles, rhombuses and squares are special kinds of parallelograms.
Rhombus : A rhombus is a quadrilateral that has four equal length sides. Every rhombus is a parallelogram.
Straight angle : A straight angle is an angle equal to $180^{\circ}.$
Choose all statements that are true for a rhombus.