Here we will use the lengths of the medians to legs of a right triangle to find the length of the hypotenuse and the length of the legs of the triangle. This will also enable us to find the length of … [Read more...] about Medians to Legs of a Right Triangle

# Right Triangles

A triangle in which one of the edges is perpendicular to another, forming a 90° angle is called a “Right triangle”:

The two edges which form the right angle (a and b) are called the “legs”, and the third edge (c), opposite the right angle, is called the hypotenuse.

The properties of right triangles, which we will prove, are the things we will use in problems involving right triangles. These include:

1. The Pythagorean theorem: a^{2}+b^{2} = c^{2} – this will be useful in any problem that asks us to find the edge lengths or areas of shapes made up of one or more right triangles.

2. The length of the median – a line that connects a vertice (or corner) of a triangle to the mid-point of the opposite side – to the hypotenuse is equal to half the length of the hypotenuse. We will use this whenever we see the median in a problem or the mid-point of the hypotenuse being used.

3. The sum of the two angles that are not the right angle is 90° (since the sum of all the angles is 180 °, and the right angle is 90°, so the other two must sum up to 180°-90°= 90°). We’ll use these in problems involving finding angle sizes in right triangles.

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*Now that we've explained the basic concept of right triangles in geometry, let's scroll down to work on specific geometry problems relating to this topic.*

## 30-60-90 Triangle

A 30-60-90 triangle is a right triangle with angles that measure 30 degrees, 60 degrees, and 90 degrees. It has some special properties. One of them is that if we know the length of only one side, we … [Read more...] about 30-60-90 Triangle

## Right Triangles: Median to the Hypotenuse is Equal to Half the Hypotenuse

In today's geometry lesson, we will prove that in a right triangle, the median to the hypotenuse is equal to half the hypotenuse. The median of a triangle is a line drawn from one of the vertices … [Read more...] about Right Triangles: Median to the Hypotenuse is Equal to Half the Hypotenuse

## 45 45 90 Triangle

A 45 45 90 triangle has unique properties. Here's a good strategy for solving multiple-step geometry problems that involve it. A right triangle has one angle which is 90°, so the sum of the other … [Read more...] about 45 45 90 Triangle