Lesson 7.4: Standard definitions of polygons and geometric properties

This lesson is all about vocabulary. Hopefully, these are all terms that you knew before, and I'm just reminding you and refreshing your memory.

Polygons 

Polygons are one of the largest named groups of geometric shapes. A polygon is a closed shape, that doesn't cross itself, that is made of straight sides connected end-to-end.

Properties (the ones you are most likely to encounter):

In this list, the words in bold are the ones that are most likely to be introduced first. Words in italics are often used to represent the mathematical vocabulary words in early grades.

A shape can have angles, and each angle can have properties:

• An angle can be right (90°)
• acute (smaller than a right angle, less than 90°)
• obtuse (wider than a right angle, more than 90°, but less than 180°)
• straight (180°)
• An angle in a closed shape like a polygon can be a reflex angle (more than 180° interior angle)

Angles within a shape can be compared. Pairs of angles can be described as being:

• adjacent (next to each other--sharing a side)
• opposite (equal numbers of sides between them as you go around the shape both ways)
• congruent (the same size)
• complementary (add up to 90°)
• supplementary (add up to 180°)

These words are usually used together to describe a property of a shape. For example, a (carefully stated) property would be: "the shape has at least one pair of opposite equal angles" or "the shape has two adjacent angles that are right angles"

A shape can have sides. The sides of a 2-dimensional shape are called edges. Edges can be straight or curved. The sides of a 3-dimensional shape are called faces. The line where two faces meet on a 3D shape is also called an edge. Faces can be flat or curved. The corner point in an angle is called a vertex (the plural of vertex is vertices).

Pairs of sides in a (2-dimensional) shape can be compared. Pairs of sides can be

• Adjacent (next to each other--sharing a vertex/angle/corner)
• Opposite (separated by an equal number of sides as you go around the shape both ways)
• congruent (same size)
• parallel (when extended, the lines the sides are on never meet)
• perpendicular (when extended, the lines the sides are on meet at a right angle)

Examples: "the opposite sides of the shape are parallel", "two pairs of adjacent sides are congruent"

Horizontal and vertical are important words, but they aren't geometric properties that would be used to define shapes because they describe how the shape looks from a particular orientation, and they change if you turn the shape to a different orientation.

Some properties of shapes describe the whole shape and not just a side or angle. A shape can be:

• 2-dimensional
• 3-dimensional
• concave (has a part that caves in so that a line stretched from one point on the shape to another doesn't stay inside the shape. A concave polygon is one that has a reflex angle.)
• convex (has no concave parts/reflex angles)
• symmetric, which could mean any of the following (though usually it means the first one, unless other conditions are specified):
  • has (at least one) line of symmetry
  • has (a specified number) of lines of symmetry
  • has rotational symmetry