Triangles
(taken from mathsisfun.com)
A triangle has three sides and three
angles
The three angles always add to 180°
Equilateral, Isosceles and Scalene
There are three special names given to triangles that tell how many sides (or angles) are equal.
There can be 3, 2 or no equal sides/angles:
Equilateral Triangle
Three equal sides
Three equal angles, always 60°
Isosceles Triangle
Two equal sides
Two equal angles
Scalene Triangle
No equal sides
No equal angles
What Type of Angle?
Triangles can also have names that tell you what type of angle is inside:
Acute Triangle
All angles are less than 90°
Right Triangle
Has a right angle (90°)
Obtuse Triangle
Has an angle more than 90°
Note, every triangle has at least 2 acute angles. It is the 3rd angle that can be acute, right, or obtuse!
Note, a triangle can have only one right or one obtuse angle… if it had 2 then you would have already
have used up the 180 degrees that a triangle sums up to.
Combining the Names
Sometimes a triangle will have two names, for example:
Right Isosceles Triangle
Has a right angle (90°), and also two equal angles
Can you guess what the equal angles are?
Naming Triangles
The name of a triangle in a diagram can be given by using the vertices (just like with
angles). The only difference with a triangle is that we use the triangle symbol, △,
rather than the angle symbol, ∠.
e.g. The diagram below has 3 triangles. The triangle on the left has the name △ABC.
It has 5 other names too: △ACB, △BAC, △BCA, △CAB, and △CBA. The reason for
this is that you can start anywhere (at A, B, or C) and then go clockwise or
anticlockwise and still make the triangle.
The middle triangle has 6 names: △ACD, △ADC, △CAD, △CDA, △DAC, △DCA.
The triangle on the right has 6 names: △CDE, △CED, △DCE, △DEC, △ECD, △EDC.
All triangles have 6 names based on its 3 vertices.