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How To Find the Height of a Triangle in 3 Different Situations

how to find height of a triangle: what each side of a triangle is called

In trigonometry, the height of a triangle can be determined in many different ways depending on whether it's a right triangle, isosceles triangle (a triangle with two equal sides), or equilateral triangle.

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What Is a Right Angle, and Why Is It Important?

what is a right angle: Diagram of three different triangles

If you’ve heard the term “right angle” in geometry class and wondered, “What is a right angle?” you’ve come to the right place. Here, we’ll define right angles, their properties, how they form, and how they convert to radians.

First, let’s define a right angle. In trigonometry, different types of angles are defined by their angle measurements. A right angle is 90 degrees. An acute angle is less than 90 degrees. An obtuse angle is more than 90 degrees.

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What Makes Two Shapes Similar Figures?

Two figures are considered to be "similar figures" if they have the same shape, congruent corresponding angles (meaning the angles in the same places of each shape are the same) and equal scale factors. Equal scale factors mean that the lengths of their corresponding sides have a matching ratio. Knowing how to identify similar figures makes it easier to prove geometric theorems and postulates.

There's a difference between similar and congruent figures. Two shapes are congruent when they are the same exact size and have the same angle measurements. Similar figures, on the other hand, do not have to be the same size.

Below is an example of similar shapes:

similar figures: Diagram showing two similar shapes

Although they are different sizes, triangle ABC and triangle DEF are considered similar triangles because they have proportional shapes and angles. Triangle ABC is simply an enlargement of DEF.

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How To Find the Vertex of a Parabola

find vertex of parabola: Graph of a quadratic equation

To find the vertex of a parabola, you first need to know how to graph quadratic equations. When graphing these, remember that every quadratic function can be put into a standard form (more on this later). This allows you to find the leading coefficient and solve for the x-intercepts. The x-intercept and y-intercept are points on the graph where the parabola intersects the x-axis or y-axis.

Putting the quadratic function into standard form will also let you find the axis of symmetry, the line that runs through the vertex and divides the parabola in half. You can then find the x-coordinate and y-coordinate of the vertex, which is the highest or lowest point on a parabola.

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What Is the Pythagorean Theorem and When Is It Used?

What is the Pythagorean theorem: Graph of how the sum of the squares creates the right triangle ABC

What is the Pythagorean theorem? It’s a trigonometry equation used to find the length of one side of a right triangle. Though similar concepts had been discovered by the Babylonians, Greek Mathematician Pythagoras was the first person to come up with a geometric proof about how the sum of the squares of the lengths can determine the side lengths of a right triangle.

Pythagoras determined that when three squares are arranged so that they form a right angle triangle, the largest of the three squares must have the same area as the other two squares combined. In the picture below, you can see how the sum of the squares creates the right triangle ABC.

This realization about the area of the squares led to the Pythagoras theorem:

What is the Pythagorean theorem: a2+b2=c2 formula

Squares are different from other parallelograms and trapezoids because all their sides are equal lengths. So since squares are made up of four equal sides, you can see that each individual square makes up a side of the right triangle.

The length of the largest square, which we'll call length c, is the length of the hypotenuse. (The hypotenuse is the longest side of a right triangle.) The smaller squares make up the other two sides of the right triangle.

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