Count : To count means to find out the number of objects by adding one for every object.

Cup : A unit to measure volume. A cup is defined as half a pint. A cup is about 0.24 liters.

Pint : A pint is a unit for measuring volume. 2 pints are a quart, and 2 cups are a pint.

Quart : A quart is a unit for measuring volume. 2 pints are a quart and 4 quarts are a gallon.

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.

Foot : A foot or ft is a unit for measuring length. 3 feet are one yard. 1 foot is about 30 $cm.$

Hypotenuse : The hypotenuse in a right triangle is the side of the right triangle that does not have any endpoints at the corner with the right angle. The hypotenuse is the longest side in a right triangle and its length can be calculated from the other two side lengths using the Pythagorean theorem.

Leg of a right triangle : A leg of a right triangle is one of the two sides in a right triangle that form the right angle.

Length : Length is the attribute of a one-dimensional shape that can be measured with a measuring tape.

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.

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.

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.

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 $\sqrt{9}=3.$

Sum : A sum is the result of an addition.