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How You Use the Triangular Proportionality Theorem Every Day

Diagram showing the triangle proportionality theorem

The triangle proportionality theorem is a geometric law stating that when you draw a line parallel to one side of a triangle, it’ll intersect the other two sides of the triangle and divide them proportionally. Regardless of whether they're obtuse, acute, or right triangles, this theorem can be used to determine unknown lengths within similar triangles.

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Three Types of Geometric Proofs You Need to Know

geometric proofs: Diagram showing a two column proof

Geometric proofs are given statements that prove a mathematical concept is true. In order for a proof to be proven true, it has to include multiple steps. These steps are made up of reasons and statements.

There are many types of geometric proofs, including two-column proofs, paragraph proofs, and flowchart proofs. We’ll walk you through each type.

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One-to-One Functions: The Exceptional Geometry Rule

one-to-one function: Function F diagram

You need to understand one-to-one functions to grasp other concepts, like inverse functions. But first, let’s start with the definition of a function. A function is a geometric rule that shows a relationship between two sets of numbers. These ordered pairs of numbers are called the domain of the function (the input values) and the range of the function (the output values). In any given function, only one output value can be paired with a given input value.

See Function F below. This set of numbers is a function because no two outputs, or range values, have the same input, or domain values. However, it isn’t a one-to-one function. Let’s explore what this is.

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What Is the Converse of the Pythagorean Theorem?

converse of the pythagorean theorem: types of triangle

The converse of the Pythagorean Theorem tells us that by comparing the sum of the squares of two sides of a triangle to the square of its third side, we can determine whether that triangle is an acute, right, or obtuse.

To review, the Pythagorean Theorem is one of the most famous theorems in trigonometry and helps us determine the sides of a right triangle. Some other formulas you might need for triangle relate to finding the base of a triangle and the area. Here are additional articles on how to find the area of a right triangle and one on how to find the third side of a triangle.

Read on to figure out how the converse of the Pythagorean Theorem works!

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The Benefits of Finding a Great Online Music Tutor

Music tutor: A female student with her teacher playing the piano

Whether you're a young violinist looking to build new skills or an experienced composer interested in music theory, finding a qualified and experienced music tutor will be central to your journey in the field of music. A high-quality music teacher or tutor will not only build fundamental skills but will also introduce you to new techniques and styles.

For musicians young and old, the best music tutor is the one who can inspire you to take your craft to the next level. Unlike subject area studies like math or history, music is an art, and it takes a special kind of person to nurture the artist in you.

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