Content Vocabulary
A transformation is the change in the size or position of a figure.
A translation is one type of transformation. It is a transformation in which all points in the figure are moved the same direction and same distance.
Congruent means having the same measure. Two figures are congruent if their corresponding side lengths and angles are the same measure.
a reflection is another type of transformation. It is a transformation that "flips" a figure over a line of reflection. It creates a mirror image of the figure. The resulting figure will be congruent to the original figure.
A rotation is another type of transformation. It is a transformation that "turns" a figure about a fixed (unchanging) point called the center of rotation. You can rotate a figure clockwise (the direction of a clock) or counterclockwise (the opposite direction of the clock). For our purposes, we will rotate figures either 90, 180, 270, or 360 degrees. You can think of these as how far to turn the image or figure. Rotations do not change the size or shape of the figure and will therefore result in congruent figures.
A dilation is a transformation that changes the size of the figure, but not the shape. The figure is either reduced (scale factor less than 1) or enlarged (scale factor greater than 1). The coordinates are both multiplied by the scale factor to determine new coordinates. The two figures would be SIMILAR.
Similar figures are figures that have the same angle measures, but have different sizes. The two figures are similar if the corresponding side lengths are proportional.
Exponent/Power- The number of times a base is multiplied by itself. The "small number" written above the base.
Base-The number being raised to a power. The "big number".
Square Root the inverse of "squaring a number". You are asking yourself to find a number that when squared equals this number.
Perfect Squares are square roots that result in a whole number answer. They are rational.
Perfect Cubes are cube roots that result in a whole number answer. They are rational.
Cube Root the inverse of "cubing a number". You are asking yourself to find a number that when cubed will equal this number.
Rational Number-Any number that can be written as a fraction.
Irrational Number-Any number that can't be written as a fraction.
Legs-The two sides of the right triangle that come together to form the right angle. They are the a and b in the Pythagorean Theorem.
Hypotenuse-The longest side of a right triangle. It is the side directly across from the right angle. It is represented by the c in the Pythagorean Theorem.
Pythagorean Theorem states that for any right triangle, the sum of the areas of the squares on the two smaller sides (legs) is equal to the area of the square on the largest side (the hypotenuse).
Converse of the Pythagorean Theorem-IF the Pythagorean Theorem is true (the sum of the squares of the two smaller sides does equal the square of the hypotenuse), then you have a right triangle.
Relation is a set of ordered pairs of inputs and outputs.
Function is a relation that maps one input to one and only one output.
Input/X value/independent variable: The first coordinate in a set of ordered pairs.
Output/y value/dependent variable: The second coordinate in an ordered pair whose value is determined by another variable.
Domain: The list of all inputs for a relation.
Range: The list of all outputs for a relation.
Slope: The "steepness" of a line. It tells you how to "move" from one point to another on the line.
Y-Intercept: The point at which the line crosses the y axis.
Slope Intercept form of a line: A linear equation in the form y=mx+b where m represents the slope and b represents the y intercept.