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.
Cos : The cosine of an angle $0\leq\alpha\leq 180^{\circ}$ or $\cos \alpha$ is defined by finding a right triangle with angle $\alpha$ and dividing the length of the leg adjacent to $\alpha$ by the length of the hypotenuse. For arbitrary angles the cosine function can be extended in a periodic way by inscribing the right triangle in a circle. The cosine can be used to calculate unknown side lengths in a triangle via the cosine law and in the case of right triangles via its definition. The Pythagorean theorem implies that $\cos^2 \alpha+\sin^2 \alpha=1.$
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 $x=1.$
Number : A number $x$ is a mathematical symbol representing a quantity.
Point : A point is an element in a space. Shapes are made of sets of points.
Positive : Positive means $\geq 0.$
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.
Sin : The sine of an angle $0\leq\alpha\leq 180^{\circ}$ or $\sin \alpha$ is defined by finding a right triangle with angle $\alpha$ and dividing the length of the leg opposite to $\alpha$ by the length of the hypotenuse. For arbitrary angles the sine function can be extended in a periodic way by inscribing the right triangle in a circle. The sine can be used to calculate unknown side lengths in a triangle via the sine law and in the case of right triangles via its definition. The Pythagorean theorem implies that $\cos^2 \alpha+\sin^2 \alpha=1.$
Square : A square is a quadrilateral with four right angles and four equal length sides. A square is a special case of a rectangle and a special case of a rhombus.
Square root : The square root of $x$ denoted by $\sqrt{x}$ is the positive number such that $(\sqrt{x})^2=\sqrt{x}\cdot \sqrt{x}=x.$ For example $\sqrt{9}=3.$
Squared : $x$ squared refers to the number $x^2=x\cdot x.$ For example 3 squared equals 9.
Choose all statements that are true for positive numbers $a, b,R$ and $0\leq\alpha\leq 2\pi$.
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.
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.
Corner : A corner of a shape is a point in the shape such that this point does not lie on the line segment between any two other points in the shape. Every triangle has 3 corners and every quadrilateral has 4 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.
Cyclic quadrilateral : A quadrilateral is called cyclic if all of its 4 corners lie on the same circle. In a cyclic quadrilateral opposite angles are complementary.
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.
Diagonal : A diagonal in a quadrilateral is the line segment between a corner and its opposing corner. A diagonal in a cube (or rectangular prism) is the line segment between two corners that are not part of a same face.
Length : Length is the attribute of a one-dimensional shape that can be measured with a measuring tape.
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.
Opposite angle : In a quadrilateral an opposite angle is the angle at the opposite corner of the corner where the angle is located.
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.
Perpendicular line : Two lines are called perpendicular if they cross in a right angle.
Quadrilateral : A quadrilateral or quadrangle is a polygon with four corners. Rectangles, trapezoids, kites, rhombuses, squares and parallelograms are all specific kinds of quadrilaterals. The sum of the interior angles in a quadrilateral is always $360^{\circ}.$
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 $180^{\circ}.$
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 quadrilateral ABCD is called cyclic if all of its points lie on a circle. Choose all statements that are true for a cyclic quadrilateral.
Inch : An inch or $in$ is a unit of measurement for length. 12 inches are one foot and 1 inch is about 2.54 $cm.$
Interior angle : An interior angle at the crossing of two parallel lines by a third line means any of the angles between the two parallel lines. An interior angle of a polygon is any of the angles at any of the corners of the polygon that lies within the polygon.
Line segment : A line segment AB is a one-dimensional shape consisting of the points A and B and all the points on the straight connection of A and B. A and B are both endpoints of the line segment AB.
Parallel : Two lines in a two-dimensional plane are called parallel if they never cross.
Ratio : A ratio is a comparison of two numbers using a division.
Similarity : Two shapes are called congruent if they have the same shape and size. Corresponding angles are the same in similar shapes and the ratio of corresponding side length is constant.
A line PQ and a line XY cross each other in a point O. The line PX is parallel to the line QY. The lengths of the line segments PX,QY, and OX in inches are 5,20 and 4. What is the length of the line segment OY in inches?