Classifying Triangles Otherwise known as making triangles feel important by giving them hard to pronounce names

So what is classifying? Basically it involves: (not a technical definition) Observing a group of things Putting them into groups with similar characteristics.

So let’s observe some triangles What characteristics do all of these triangles have that we can use to classify them? # of Sides # of angles Angles Vertices Side Length Not all of these are helpful since some characteristics are true of all triangles and won’t help us subdivide them These symbols just represent the angle for that vertex This symbol means that this angle is a right angle which means it is 90° We can cross out the ones that all triangles have exactly the same So we will classify based on angles and side length

So let’s learn to classify by angle first… When classifying by angle, you classify by the biggest angle in the triangle!!! So I will be using the following angles to classify these triangles These angles are all the same so we can use any Remember the 3 kinds of angles are: Obtuse which is greater than 90° Right which is equal to 90° Acute which is less than 90°

So let’s learn to classify by angle first… Looking at the first one, it looks like we would have all angles which are less than 90 ° Remember the 3 kinds of angles are: Obtuse which is greater than 90° Right which is equal to 90° Acute which is less than 90° So this triangle would be…. Looking at the second triangle, it looks like our biggest angle would be exactly 90 ° So this triangle would be…. Looking at the third triangle, it looks like our biggest angle would be more than 90 ° So this triangle would be….

Try these triangles by yourself. Classify them by angle ACUTE OBTUSE RIGHT

Brain Break

Now let’s learn to classify by side length There are 3 relationships that the sides can have with one another… All 3 can be the same length which makes an equilateral triangle 2 sides can be the same length which makes an isosceles triangle No sides are the same length which would make a scalene triangle Try to determine what each of the triangles to the left are. For this triangle 2 sides have the same length, so this is an…. For this triangle no sides have the same length, so this is a…

Try to classify the following triangles by side length All 3 can be the same length which makes an equilateral triangle 2 sides can be the same length which makes an isosceles triangle No sides are the same length which would make a scalene triangle Isosceles Equilateral Scalene

You can also classify triangles by side and angle at the same time Remember the 3 side length classifications are : Equilateral: All sides are the same length Isosceles: 2 sides are the same length Scalene: No sides are the same length Remember the 3 angle classifications are: Obtuse which is greater than 90° Right which is equal to 90° Acute which is less than 90° This triangle has two sides that are the same, so it would an isosceles triangle. However, it’s biggest angle is less than 90° so it’s also acute. So this triangle is an: Acute isosceles triangle or an Isosceles acute triangle

Try to classify the following triangles by angle and side length Acute Isosceles Acute Equilateral Right Scalene Obtuse Scalene Remember the 3 side length classifications are : Equilateral: All sides are the same length Isosceles: 2 sides are the same length Scalene: No sides are the same length Remember the 3 angle classifications are: Obtuse which is greater than 90° Right which is equal to 90° Acute which is less than 90° Obtuse Isosceles

Brain Break