How Do You Write a Coordinate Proof?

How Do You Write a Coordinate Proof?

Note:

In this tutorial, you'll see how to write a coordinate proof to prove that two triangles are congruent. Check it out!

Keywords:

  • coordinate
  • coordinate plane proof
  • proof
  • quadrilateral

Background Tutorials

  • 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).

      • What is the Coordinate Plane?What is the Coordinate Plane?

      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 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.

      • What Does Congruent Mean?What Does Congruent Mean?

      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!

  • Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.

      • What is a Triangle?What is a Triangle?

      What is a Triangle?

      You can't learn everything about math without dealing with triangles. Did you know that there are different types of triangles? Check out this tutorial, and learn about triangles and their different types!

  • Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

      • What Is the Distance Formula?What Is the Distance Formula?

      What Is the Distance Formula?

      If you need to find the distance between to points on the coordinate, you'll probably use the distance formula to get your answer. This tutorial introduces you to the distance formula and even shows you how to find it!

Further Exploration

  • Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.