Classification

=**Classification** = Classification is a rhetorical function used to organize information according to categories. For example: Acute (a), obtuse (b), and straight (c) angles. Here, a and b are [|supplementary angles]. || taken from: []  =**Assignment** =
 * An angle of 90° (//[|π] ///2 radians, or one-quarter of the full circle) is called a **[|right angle] **. Two lines that form a right angle are said to be **[|perpendicular] ** or **[|orthogonal] **.
 * Angles smaller than a right angle (less than 90°) are called **acute angles** ("acute" meaning "sharp").
 * Angles larger than a right angle and smaller than two right angles (between 90° and 180°) are called **obtuse angles** ("obtuse" meaning "blunt").
 * Angles equal to two right angles (180°) are called **straight angles**.
 * Angles larger than two right angles but less than a full circle (between 180° and 360°) are called **reflex angles**.
 * Angles that have the same measure are said to be **[|congruent] **.
 * Two angles opposite each other, formed by two intersecting straight lines that form an "X" like shape, are called **<span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; padding-right: 10px;">[|vertical angles] ** or**opposite angles**. These angles are congruent.
 * <span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0.5em; padding-bottom: 0px; padding-left: 3em; padding-right: 0px; padding-top: 0px;">Angles that share a common vertex and edge but do not share any interior points are called **<span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; padding-right: 10px;">[|adjacent angles] **.
 * <span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0.5em; padding-bottom: 0px; padding-left: 3em; padding-right: 0px; padding-top: 0px;">Two angles that sum to one right angle (90°) are called **<span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; padding-right: 10px;">[|complementary angles] **. The difference between an angle and a right angle is termed the **complement** of the angle.
 * <span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0.5em; padding-bottom: 0px; padding-left: 3em; padding-right: 0px; padding-top: 0px;">Two angles that sum to a straight angle (180°) are called **<span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; padding-right: 10px;">[|supplementary angles] **. The difference between an angle and a straight angle is termed the **supplement** of the angle.
 * <span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0.5em; padding-bottom: 0px; padding-left: 3em; padding-right: 0px; padding-top: 0px;">Two angles that sum to one full circle (360°) are called **explementary angles** or **conjugate angles**.
 * <span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0.5em; padding-bottom: 0px; padding-left: 3em; padding-right: 0px; padding-top: 0px;">An angle that is part of a <span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; padding-right: 10px;">[|simple polygon] is called an **<span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; padding-right: 10px;">[|interior angle] ** if it lies in the inside of that the simple polygon. Note that in a simple polygon that is concave, at least one interior angle exceeds 180°. In <span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; padding-right: 10px;">[|Euclidean geometry], the measures of the interior angles of a <span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; padding-right: 10px;">[|triangle] add up to //π// radians, or 180°; the measures of the interior angles of a simple <span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; padding-right: 10px;">[|quadrilateral] add up to 2//π//radians, or 360°. In general, the measures of the interior angles of a <span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; padding-right: 10px;">[|simple polygon] with //n// sides add up to [(//n// − 2) × //π//] radians, or [(//n// − 2) × 180]°.
 * <span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0.5em; padding-bottom: 0px; padding-left: 3em; padding-right: 0px; padding-top: 0px;">The angle supplementary to the interior angle is called the **<span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; padding-right: 10px;">[|exterior angle] **. It measures the amount of "turn" one has to make at this vertex to trace out the polygon. If the corresponding interior angle exceeds 180°, the exterior angle should be considered<span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; padding-right: 10px;">[|negative] . Even in a non-simple polygon it may be possible to define the exterior angle, but one will have to pick an <span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; padding-right: 10px;">[|orientation] of the <span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; padding-right: 10px;">[|plane] (or <span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; padding-right: 10px;">[|surface] ) to decide the sign of the exterior angle measure. In Euclidean geometry, the sum of the exterior angles of a simple polygon will be 360°, one full turn.
 * <span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0.5em; padding-bottom: 0px; padding-left: 3em; padding-right: 0px; padding-top: 0px;">Some authors use the name **exterior angle** of a simple polygon to simply mean the explementary (//not// supplementary!) of the interior angle <span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; padding-right: 10px;">[|[1] ]. This conflicts with the above usage.
 * <span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0.5em; padding-bottom: 0px; padding-left: 3em; padding-right: 0px; padding-top: 0px;">The angle between two <span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; padding-right: 10px;">[|planes] (such as two adjacent faces of a <span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; padding-right: 10px;">[|polyhedron] ) is called a **<span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; padding-right: 10px;">[|dihedral angle] **. It may be defined as the acute angle between two lines <span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; padding-right: 10px;">[|normal] to the planes.
 * <span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0.5em; padding-bottom: 0px; padding-left: 3em; padding-right: 0px; padding-top: 0px;">The angle between a plane and an intersecting straight line is equal to ninety degrees minus the angle between the intersecting line and the line that goes through the point of intersection and is normal to the plane.
 * <span style="margin-bottom: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0.5em; padding-bottom: 0px; padding-left: 3em; padding-right: 0px; padding-top: 0px;">If a straight <span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; padding-right: 10px;">[|transversal line] intersects two <span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; padding-right: 10px;">[|parallel] lines, corresponding (alternate) angles at the two points of intersection are congruent; <span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; padding-right: 10px;">[|adjacent angles] are <span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; padding-right: 10px;">[|supplementary] (that is, their measures add to //π// radians, or 180°).

<span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; padding-right: 10px;">[]
 * I. Visit the following link and draw a graphic organizer showing the classification of triangles. Work only with the types of triangles. **


 * II. Write the classification of the mathematical term you defined and described in the last wiki activity **

For further information about writing classifications please visit the following links: <span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; padding-right: 10px;">[] <span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; padding-right: 10px;">[]

Here`s an interesting link for you to revise how math can be defined and classified, and how its different areas can be described. <span style="background-attachment: initial; background-clip: initial; background-color: initial; background-origin: initial; background-position: 100% 50%; background-repeat: no-repeat no-repeat; padding-right: 10px;">[|[[http://www.math.niu.edu/%7Erusin/known-math/index/beginners.html|http://www.math.niu.edu/~rusin/known-math/index/beginners.html] ]]


 * ANSWERS:**

I. Classification of Triangles:


 * || ** Equilateral: ** || ** Isosceles: ** || ** Scalene: ** ||
 * Sides || Three sides. || Three sides. || Three sides. ||
 * Sides’ length || All sides are equal. || Two sides are equal. || None of the sides are equal. ||
 * Angles || All are congruent and acute. || All are acute angles. || The angles can be obtuse, straight, or acute. ||
 * Interior angles || All angles sum 180° exactly. || All angles sum 180° exactly. || All angles sum 180° exactly. ||
 * Polygon || Regular polygon. || Irregular polygon. || Irregular polygon. ||
 * Symmetry || Symmetric figure. || Symmetric figure. || Asymmetric figure. ||

II. Classification of the equal sign:

|| It is placed just between tw o exact things. ||  ||
 * |||| ** Equal sign:  ** ||
 * What? ||||  Mathematical symb o l.  ||
 * Use? ||||  Used t o show equality in equations.   ||
 * Invented? ||||  In 1557, by Welshman R obert.   ||
 * F orm?  ||  Tw o short horizontal lines, one over the other. =   ||   ||
 * Placed?

<span style="display: block; font-family: arial,helvetica,sans-serif; font-size: 13px; height: 600px; line-height: 1.5; min-height: 600px; overflow-x: auto; overflow-y: visible; padding-bottom: 2em; width: 807px;">This is what I wrote: The equal sign, =, is a mathematical symbol used to show equalities. This useful symbol is used to state that two or more things are exactly the same, as used in an equation. The equal sign was invented in 1557 by a mathematician named Welshman Robert. The equal sign is formed by two short horizontal lines, one under the other, and it is placed between the equalities.