Unit 5 Visual Glossary by: Hannah Lee
Concave Polygon: A polygon in which at least one diagonal is in the exterior of the polygon or if any part of the diagonal is in the exterior of the polygon. An easy way to differentiate between convex and concave is that a concave polygon usually caves in. There is no symbol or notation for a concave polygon.
Convex Polygon: A polygon in which all the diagonals are within the interior of the polygon and no diagonals are in the exterior of the polygon. There is no symbol or notation to show when a polygon is convex.
Regular Polygon: A polygon in which all the angles are congruent and all the sides are congruent. In other words, a regular polygon is both equiangular and equilateral. There is no symbol to denote a regular polygon.
Parallelogram: A quadrilateral that has two pairs of parallel sides. The sides that are parallel are opposite each other. In addition to those properties, the sides that are parallel to each other are also congruent to each other. Therefore, a parallelogram has two pairs of parallel, opposite, and congruent sides. In a parallelogram, diagonals also bisect each other, and the angles that are opposite in a parallelogram are congruent to each other. The symbol for a parallelogram is ▱.
Rectangle: A parallelogram in which all the angles are congruent. Since all the angles are congruent, each angle is 90°, making them right. Like stated above, a rectangle is a parallelogram, which means that it shares all the properties of a parallelogram, which means that it has two pairs of parallel and congruent sides, opposite angles that are congruent, and diagonals that bisect each other. Rectangles also have diagonals that are congruent to each other. Unlike the parallelogram, there is no symbol or notation for the rectangle.
Rhombus: A parallelogram in which all the sides are congruent. The angles do not necessarily have to be congruent. Since the rhombus is a parallelogram, it shares all the properties of a parallelogram, which means that it has two pairs of parallel and congruent sides, opposite angles that are congruent, and diagonals that bisect each other. Furthermore, the rhombus also have diagonals that are perpendicular to each other and that bisect opposite angles. Unlike the parallelogram, the rhombus does not have a symbol or notation.
Square: A parallelogram in which all the angles are congruent and all the sides are congruent. Squares, unlike other quadrilaterals, are also parallelograms, rectangles, and rhombi. Since a square is also considered to be a parallelogram, rectangle, and rhombus, it shares all of the properties of a parallelogram, a rectangle, and a rhombus. There is no symbol or notation for the square.
Diagonal: A line segment that connects two non-consecutive vertices. Diagonals can be found in all the polygons, from triangles to undecagons. However, there is no symbol or notation for diagonals.
Kite: A quadrilateral that has two pairs of consecutive, congruent sides. In a kite, the diagonals are perpendicular, and they bisect exactly one pair of opposite angles. There is no symbol or notation to represent that a shape or a quadrilateral is a kite.
Trapezoid: A quadrilateral that has exactly one pair of parallel sides. There is no symbol or notation for the trapezoid.
Isosceles Trapezoid: A trapezoid in which the legs, or the sides of the trapezoid that are not parallel are congruent to each other and the base angles, or the two consecutive angles in which the common side is a base, are congruent. The diagonals of an isosceles trapezoid are also congruent. There is no symbol for an isosceles trapezoid.
Midsegment of a Trapezoid: A segment in which its two endpoints are the midpoints of the legs of the trapezoid. There is no symbol or notation for a midsegment.
Apothem: A line segment in which its endpoints are the center of the polygon and the midpoint of one of the sides of the polygon. In addition, the apothem is also perpendicular to the side of the polygon. There is no symbol or notation for the apothem. However, in the area formula of a regular polygon, the apothem is represented by a lowercase "a".
Similarity Ratio: Ratio of the sides. The similarity ratio is equal to the ratio of the sides, heights, perimeters, or circumferences. The area, however, is equal to the similarity ratio squared. There is no symbol or notation for the similarity ratio.
I chose these terms because the general theme of this unit was polygons, especially quadrilaterals. I feel that all these terms were important to know and understand in order to have been successful in this unit. Not only do most of these terms only show up for one lesson, but they show up on other lessons, and many will probably make a reappearance some time later in another unit, once again emphasizing its importance.