Amy has a master's degree in secondary education and has taught math at a public charter high school.
After watching this video lesson, you will be able to identify all kinds of triangles. You'll learn the identifying factors of each type of triangle, including the kinds of angles and lines to look for.
In this lesson, we're talking about triangles. Triangles are two-dimensional shapes with three straight sides and three angles. There are many kinds of triangles that you will come across. You will come across triangles in your math and geometry classes, and you will see them all around if you look for them. You might see triangle shapes keeping a bridge up and you might see triangle shapes supporting the roofs on houses. We can describe our triangles in six different ways; all of our triangles will belong to at least one of these six different categories. Let's take a look.
The first is the equilateral triangle. It is a triangle with three equal sides. Because all three sides are equal, this triangle will also have three equal angles. Each angle of the equilateral triangle will always equal 60 degrees. This is because triangles' angles always add up to 180 degrees. Thus, if all three angles are equal, we can divide that 180 by 3 to get 60 degrees for each angle. If you see a triangle with all equal sides and equal angles, then you are looking at an equilateral triangle.
The second is an isosceles triangle. This type of triangle has two equal sides. Because this triangle has two equal sides, it will also have two equal angles. The two equal angles are the angles opposite the two equal sides. In this type of triangle, unlike the equilateral triangle, the two equal angles do not have to be a certain degree. They can be any measurement under 90 degrees.
The third is a scalene triangle. A scalene triangle's a triangle with no equal sides. Because there are no equal sides, this triangle will also have no equal angles. This means that all the sides are different lengths and all the angles are different measurements.
The fourth is the acute triangle. This triangle has all angles less than 90 degrees. In this type of triangle, there can be two or three equal angles as long as they are all less than 90 degrees. You can also have an acute triangle where none of the angles are equal.
The fifth is the right triangle. A right triangle is a triangle with one 90-degree angle. As long as the triangle has that one 90-degree angle, then it is a right triangle. It doesn't matter what the angles measure.
Our last and sixth category is the obtuse triangle. This is a triangle with one angle that measures more than 90 degrees. Just like the right angle, it doesn't matter what the other angles measure.
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The first three categories - equilateral, isosceles, and scalene - tell you what kind of triangle you will have based on the side lengths and how many equal angles there are. The last three categories - acute, right, and obtuse - tell you what kind of triangle you have based on the angle measurements. It is possible for your triangle to belong to more than one category. Let's take a look.
What kind of triangle is this?
Looking at this triangle, we see that it has two equal sides. Because this triangle has two equal sides, it also has two equal angles. This means this triangle is an isosceles triangle. We don't know anything about the angle measurements, so we can't say anything more about this triangle.
What about this triangle?
This triangle has one 90-degree angle and no equal sides. The one 90-degree angle makes this triangle a right triangle. The no equal sides make it a scalene triangle. So, this triangle is both a scalene triangle and a right triangle.
Let's review what we've learned.
Triangles are two-dimensional shapes with three straight sides and three angles. An equilateral triangle is a triangle with three equal sides. An isosceles triangle is a triangle with two equal sides. A scalene triangle is a triangle with no equal sides.
An acute triangle is a triangle that has all angles less than 90 degrees. A right triangle is a triangle with one 90-degree angle. An obtuse triangle is a triangle with one angle that measures more than 90 degrees.
All triangles will belong to at least one of these groups. It is possible for a triangle to belong to more than one of these groups.
With review of the lesson and some practice, you could realize the following goals:
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