Polygons. Polygons. Definition:. A closed figure formed by line segments so that each segment intersects exactly two others, but only at their endpoints. These figures are not polygons. These figures are polygons. Classifications of a Polygon. Convex:.
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A closed figure formed by line segments so that each segment intersects exactly two others, but only at their endpoints.
These figures arenot polygons
These figures are polygons
No line containing a side of the polygon contains a point in its interior
A polygon for which there is a line containing a side of the polygon and a point in the interior of the polygon.
A convex polygon in which all interior angles have the same measure and all sides are the same length
Two sides (or two interior angles) are not congruent.
A triangle in which all 3 sides are different lengths.
AC = 3.47 cm
AB = 3.47 cm
AB = 3.02 cm
AC = 3.15 cm
A triangle in which at least 2 sides are equal.
GI = 3.70 cm
GH = 3.70 cm
A triangle in which all 3 angles are less than 90˚.
Classification by Sides
with Flow Charts & Venn Diagrams
Classification by Angles
with Flow Charts & Venn Diagrams
Two sets of parallel sides
Two sets of congruent sides.
The angles that are opposite each other are congruent (equal measure).
Has all properties of quadrilateral and parallelogram
A rectangle also has four right angles.
A rectangle can be referred to as an equiangular parallelogram because all four of it’s angle are right, meaning they are all 90° (four equal angles).
A rhombus is sometimes referred to as a “slanted square”.
A rhombus has all the properties of a quadrilateral and all the properties of a parallelogram, in addition to other properties.
A rhombus is often referred to as a equilateral parallelogram, because it has four sides that are congruent (each side length has equal measure).
Unlike a parallelogram, rectangle, rhombus, and square who all have two sets of parallel sides, a trapezoid only has one set of parallel sides. These parallel sides are opposite one another. The other set of sides are non parallel.
One can never assume a trapezoid is isosceles unless they are given that the trapezoid has specific properties of an isosceles trapezoid.
Isosceles is defined as having two equal sides. Therefore, an isosceles trapezoid has two equal sides. These equal sides are called the legs of the trapezoid, which are the non-parallel sides of the trapezoid.
Both pair of base angles in an isosceles trapezoid are also congruent.
It’s important to have a good understanding of how each of the quadrilaterals relate to one another.
Any quadrilateral that has two sets of parallel sides can be considered a parallelogram.
A rectangle and rhombus are both types of parallelograms, and a square can be considered a rectangle, rhombus, and a parallelogram.
Any quadrilateral that has one set of parallel sides is a trapezoid. Isosceles and Right are two types of trapezoids.