A triangle is a geometric shape made up of three sides and three angles.
There are three special names given to triangles that tell you how many sides and angles are equal to one another.
In a triangle, there can be 3, 2, or no equal sides and angles.
The three types of triangles are:
1. Equilateral Triangles, which have three equal sides and three equal angles always equal to 60 degrees.
2. Isosceles Triangles, which have two equal sides and two equal angles.
3. Scalene Triangles, which have no equal sides and no equal angles.
Triangles may also have names which describe the type of angle which they contain:
1. An acute triangle will have all three angles less than 90 degrees.
2. A right triangle will have one right angle, which is an angle of 90 degrees.
3. An obtuse triangle will have one angle which is greater than 90 degrees.
When we name a triangle, we can combine these names in order to give as much information about the triangle as possible.
For example: Consider a right isosceles triangle.
The word right in the name tells us that this triangle will have one 90 degree angle.
The word isosceles in the name tells us that two sides of the triangle are equal and two of the angles of the triangle are equal.
From this information we know how the triangle must look.
In a right isosceles triangle, one angle will be 90 degrees and the other two angles will be 45 degrees.
Finding the Perimeter of a Triangle
The perimeter is the distance around the edges of the triangle. In order to find the perimeter of the triangle, all we need to do is add up the lengths of the three sides of the triangle.
Example: C
A B
If side AC = 4 cm, side CB = 5 cm and side AB = 7 cm, then we have that the perimeter of this triangle is equal to:
perimeter = 4cm + 5 cm + 7cm = 16cm
Finding the Area of a Triangle
The area of a triangle is half of the base times the height.
Here is a formula you can always use when finding the area of a triangle:
A = ½ (b)(h)
In this formula, “b” is the distance along the base and “h” is the height of the triangle measured at right angles to the base.
Example:
If we know that they height of the triangle is 5 cm and that the base of the triangle is 12 cm, then we can apply the area formula in order to solve for the area of the triangle.
A = ½ (b) (h) = ½ (5 cm) (12 cm) = 30 cm squared
Properties of Triangles
1. Interior angles (angles on the inside) sum up to 180 degrees.
2. Triangle Inequality Theorem: This theorem states that the sum of the lengths of any 2 sides of a triangle must be greater than the third side.
3. Relationship between measurement of the sides and angles in a triangle: the largest interior angle and side are opposite each other. The same rule applies to the smallest sized angle and side and the middle sized angle and side.
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This article was written for you by Mia, one of the tutors with Test Prep Academy.