Identidades dos triângulos retângulos

Identifying Right Triangles

A right triangle is a triangle that contains a right angle ($90^{\circ}$). There are a few different ways to identify right triangles, depending on the information you've been given. Let's take a look!

The first (and easiest) way to identify a right a triangle is if it's already been marked with a $90^{\circ}$ angle, like the one above. Even if $90^{\circ}$ isn't written in, if you see a little square drawn in the corner, that's also a way of indicating a right angle.

You can also determine if a triangle is a right triangle if you're given degree measurements for two of the triangles angles.

Another way to identify a right triangle is by using the Pythagorean Theorem. The Pythagorean Theorem shows the relationship among the lengths of the sides of a right triangle.

$$a^2+b^2=c^2$$

c is called the hypotenuse, and its the side that is across from the right angle. a and b are the lengths of the other two sides.

If you plug in the lengths of each side of the triangle into the Pythagorean equation and get a TRUE statement, then the triangle is a right triangle.

$$3^2+4^2\overset{?}{=} 5^2$$ $$9+16\overset{?}{=} 25$$ $$25=25$$

This produces a true statement ($25=25$), which tells us that our triangle is in fact a right triangle.

A right triangle is a triangle in which one of the angles is a $90^{\circ}$ angle.

A triangle can be determined to be a right triangle if the side lengths are known. If the lengths satisfy the Pythagorean Theorem ($a^2+b^2=c^2$) then it is a right triangle.

For example, if it is known that a triangle has side lengths of $11$, $60$, and $61$, we can show that the sides satisfy the Pythagorean Theorem: $$11^2 + 60^2 \overset{?}{=} 61^2$$ $$121 + 3600 \overset{?}{=} 3721$$ $$3721 = 3721$$

The side lengths $3$, $8$, and $10$ WOULD NOT be side lengths of a right triangle: $$3^2 + 10^2 \overset{?}{=} 20^2$$ $$9 + 100 \overset{?}{=} 400$$ $$109 \neq 400$$

(Video) Triangles

by Math Antics

Here's a video by mathantics explaining how you can tell if a triangle is a right triangle.

$\large{\text{Summary}}$

Triangles can be classified by their sides or by their angles. The three types of angles are acute, right, and obtuse. So we classify triangles based on if they have an obtuse angle, right angle, or acute angle. So a right triangle has a right angle which means it has a $90^{\circ}$ angle. All triangles have at least two acute angles so its the third angle that we look at to tell what kind of triangle it is.