Properties of Triangles A triangle is a polygon with three sides and three angles. The properties of triangles are a set of relationships between the angles...
Properties of Triangles
A triangle is a polygon with three sides and three angles. The properties of triangles are a set of relationships between the angles and sides of a triangle that hold true regardless of the position of the triangle or the values of its measurements.
The three angles of a triangle are related by the following angles:
Angles opposite the equal sides are congruent. This means that if two sides of a triangle have the same length, the angle opposite them will also have the same measure.
Angles opposite the different sides are complementary. This means that if two angles are opposite each other, their measures add up to 180 degrees.
The sum of the angles in a triangle is 180 degrees. This means that the angles of a triangle will add up to 180 degrees no matter how you arrange them.
The sides of a triangle are also related by the following properties:
The longest side is opposite the right angle. This means that the longest side of a triangle is opposite the right angle.
The shortest side is opposite the smallest angle. This means that the shortest side of a triangle is opposite the smallest angle.
The altitude from the base to the vertex divides the base into two equal parts. This means that the altitude from the base to the vertex divides the base into two equal parts.
These properties are true regardless of the position of the triangle or the values of its measurements. This means that a triangle with three equal sides will have three equal angles, and a triangle with three right angles will have three right angles