8 4 Classifying Triangles Classifying Triangles by Angles

8. 4 Classifying Triangles

Classifying Triangles by Angles Triangles can be grouped based on the types on angles they are made of. The easiest type of angle to identify is a right triangle, because it has a right angle in it!

Another type of triangle is the acute triangle. It has ONLY ACUTE ANGLES IN IT! An acute angle looks like a ‘squashed L’. These angles are less than 90.

The last type of triangle is the obtuse triangle. You can probably guess by not that it is named for the obtuse angle in it. Think about it! An acute triangle has angles that are all less than 90. A right triangle has only one right angle in it! The other angles have to be acute! Otherwise, it would look like part of a rectangle! An obtuse triangle also has only one obtuse angle in it! Looking for those angles can help decide what type of triangle you are looking at!

Can you identify these triangles? Obtuse Triangle Acute Triangle Right Triangle

Classifying Triangles by Their Sides This is an acute triangle because it’s angles are all acute. But we can also group triangles based on the comparison of the measurements of their sides. This triangle has sides that are all the same length. This diagram tells that because of the tick marks on each side. Because the sides are all the same length, this is called an equilateral triangle. ‘Equi’ means equal, and ‘lateral’ means ‘sides’. The numbers of tick marks do not tell the exact lengths of the sides, but because there are the same number of tick marks, they tell you that the measurement is the same!

This triangle has only two sides that are the same length. Only two of the sides has tick marks (two tick marks each)! We don’t know the measurement of the third side, but we do know that it is not the same as the two sides with the tick marks! This is called an isosceles triangle.

Find the measure of c 20 + 35 180 - 55 125

The third type of triangle has sides that are all of different lengths! Notice that there a different number of tick marks on all the sides. This type of triangle is called a scalene triangle.

When classifying triangles, notice what is asked for first. If you are asked to classify the triangle based on its sides and angles, then answer with the correct category for sides first, then your answer for the classification of the angles. This would be an equilateral acute triangle.

When the angle measurements of triangles are added together, they always total 180 To find the measure of angle a, then add 80 and 60 together. Then subtract your answer from 180 + 60 140 180 - 140 40 A = 40