How Do You Use the Diagonals of a Rectangle to Find the Value of a Variable?

How Do You Use the Diagonals of a Rectangle to Find the Value of a Variable?

Note:

When you make diagonals inside a rectangle, those diagonals are congruent. With this information, you can find the value of a variable that's part of a measurement of a diagonal. This tutorial shows you the steps.

Keywords:

  • problem
  • quadrilateral
  • diagonals
  • rectangle
  • variable
  • equation

Background Tutorials

  • Understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.

      • What is a Rectangle?What is a Rectangle?

      What is a Rectangle?

      A rectangle is one of the many fundamental shapes you'll see in math. Rectangles have special properties that can be very useful in helping you solve a problem. This tutorial introduces you to rectangles and explains their interesting qualities!

  • Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers).

  • 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!

  • Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.

      • What are Inverse Operations?What are Inverse Operations?

      What are Inverse Operations?

      Did you know that addition is the opposite of subtraction and that division is the opposite of multiplication? In fact, these opposite operations will undo each other! These types of operations are called inverse operations. Get a great look at inverse operations with this tutorial!

  • Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals.

      • What is a Parallelogram?What is a Parallelogram?

      What is a Parallelogram?

      A parallelogram is a special type of quadrilateral with some special properties. In this tutorial, take a look at parallelograms and learn what kinds of quadrilaterals can also be called parallelograms!