Properties of Triangles, Circles and Polygons A triangle is a polygon with three vertices and three sides. It has several important properties that defin...
A triangle is a polygon with three vertices and three sides. It has several important properties that define its shape, including the lengths of its sides and angles.
Side lengths:
The sides of a triangle are always in the same order (e.g., adjacent sides are equal in length).
The longest side is called the hypotenuse.
The shortest side is called the legs.
Angles:
The angles of a triangle add up to 180 degrees.
The sum of the angles in a triangle formed by two sides and a non-included angle is equal to the angle formed by the third side and the non-included angle.
The angles formed by the legs of a triangle are complementary, meaning they add up to 180 degrees.
Circles:
A circle is a curved shape with no corners or edges.
It has a center point that is located at the center of the circle.
The circumference of a circle is the length of its perimeter, which is the distance around the circle.
The area of a circle is calculated using the formula πr², where r is the radius of the circle.
Polygons:
A polygon is a shape with more than three sides and more than three angles.
The sum of the angles in a polygon with n sides is equal to 180 degrees.
A polygon with n sides is called a regular polygon if all of its interior angles are equal and all of its interior angles add up to 180 degrees.
A polygon with n sides is called a convex polygon if all of its angles are acute (less than 180 degrees) and all of its interior angles are less than 180 degrees.
A polygon with n sides is called a concave polygon if some of its angles are greater than 180 degrees and some of its interior angles are greater than 180 degrees