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What is a triangle? In addition to having three sides and three angles,there are four basic rules or theorems that a shape must satisfy in order to be classified as a triangle.
Theorem 1. This theorem states that when adding the side lengths of a triangle, the sum of two sides of a triangle must be greater than the length of the third side.
Types of Triangles
6 + 3 > the third side 4
4+3 > the third side 6
6+4 > the third side 3
Interior angles = 180
60 + 60 +60 = 180 degrees
Interior and Exterior angles are supplementary
Theorem 2. The sum of the interior angles of a triangle equal 180 degrees.
Theorem 3. The measure of an exterior angle is formed by extending one of the sides. Furthermore, the interior and exterior angles created, are supplementary.
Theorem 4.Proportionality of Triangles. The longest side of a triangle is opposite the largest angle, and the shortest side is opposite the smallest angle.
Triangles can be classified by the length of their sides.
Three different side lengths
Three different angle measures
At least two congruent sides
At least two congruent angles
Three congruent sides
Three congruent angles The angle measure equals 60 degrees
Triangles can also be classified by their angles.
There are three angles often associated with triangles
- Acute angles are less than 90 degrees
- Right angles are exactly 90 degrees
- Obtuse are greater than 90 degrees
All triangles have two acute angles and the third angle determines the type of
Triangle you have.
Triangle with three angles that measure less than 90 degrees
Triangle with one angle greater than 90 degrees
Triangle with one right angle ( 90 degrees)
The other two angles are complementary