Background Tutorials

• Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles.

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    What are Acute, Obtuse, and Right Triangles?

    Did you know that there are different kinds of triangles? Knowing how to identify these triangles is an important part of solving many problems involving these triangles. Check out this tutorial and learn about some of the different kinds of triangles!

• Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).

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    What is the Coordinate Plane?

    You can't graph a function or plot ordered pairs without a coordinate plane! Learn about the coordinate plane by watching this tutorial.

• Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.

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    What is an Ordered Pair?

    Ordered pairs are a fundamental part of graphing. Ordered pairs make up functions on a graph, and very often, you need to plot ordered pairs in order to see what the graph of a function looks like. This tutorial will introduce you to ordered pairs!

• Lines are taken to lines, and line segments to line segments of the same length.

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    What is a Rotation?

    Ever turned a door handle? You were performing a rotation! In math, rotations are just the same! Check out this tutorial to learn about rotations.

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    What is a Translation?

    Ever slide something across a table? If so, then you have performed a translation! In this tutorial, learn the definition of translation and see some really neat examples. Take a look!

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    What is a Transformation?

    Transformations can be really fun! They allow you to change or move a figure. In this tutorial, learn about all the different kinds of transformations!

• Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

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    What Does Congruent Mean?

    If two figures have the same size and shape, then they are congruent. The term congruent is often used to describe figures like this. In this tutorial, take a look at the term congruent!

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    What is a Reflection?

    When you look in the mirror, you see your reflection. In math, you can create mirror images of figures by reflecting them over a given line. This tutorial introduces you to reflections and shows you some examples of reflections. Take a look!

• Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

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    What is a Dilation?

    When someone's eyes dilate, their pupils get bigger or smaller, but they always stay the same shape. Dilation in math is very similar. When you dilate a figure, you change the size of the figure without changing its shape. This tutorial introduces you to dilation. Take a look!

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    How Do You Rotate a Figure 90 Degrees Around the Origin?

    Rotating a figure about the origin can be a little tricky, but this tutorial can help! This tutorial shows you how to rotate coordinates from the original figure about the origin. Then, simply connect the points to create the new figure. See this process in action by watching this tutorial!

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    How Do You Use Coordinates to Translate a Figure Vertically?

    Translating a figure on the coordinate plane is easier than you might think! This tutorial shows you how to translate coordinates from the original figure. Then, simply connect the points to create your

• Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch).

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    What is a Congruence Transformation, or Isometry?

    Not all transformations are created equal! Congruence transformations, or isometries, have a special property that distinguishes them from other transformations. This tutorial will show you what makes them special!