Answer all the questions below and press submit to see how many you got right.
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.
Intersect : Two shapes intersect if they have at least one point in common.
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.
Midpoint : The midpoint of a line segment is the point on the line segment that cuts the line segment into two equal length pieces.
Point : A point is an element in a space. Shapes are made of sets of points.
Ratio : A ratio is a comparison of two numbers using a division.
Right triangle : A right triangle is a triangle that has a right angle. The sides that form the right angle are called legs, the third side is called hypotenuse. The area of a right triangle is half the product of the lengths of the two legs. The Pythagorean theorem is an important theorem for right triangles that allows to calculate the third side of a right triangle given the other two.
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 $180^{\circ}.$
We look at a triangle with corners A,B and C. We call the sides opposite of A,B and C a, b and c and the midpoints of a,b,c D,E and F. Select all the 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.
Adjacent : Adjacent means next to each other.
Adjacent corner : Adjacent corners in a polygon are corners that are linked by a side.
Adjacent side : Adjacent sides in a polygon are sides that share a corner.
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.
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.
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.
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.
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.
Right angle : A right angle is an angle equal to $90^{\circ}.$
Set : A set is a collection of objects.
Straight angle : A straight angle is an angle equal to $180^{\circ}.$
Choose all statements that are true for a parallelogram.
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.
Constant : Constant is another word for a fixed number that is mainly used in the context of expressions or functions like $f(x)=c$ that are equal to the same number irrespective of any variable.
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 $\{(x,y)| \frac{x^2}{a^2}+\frac{y^2}{b^2}=1 \}$
Choose all statements that are true for an ellipse.