angle math definition.docx

7/28/2019 Angle Math Definition.docx

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Acute angleFrom Latin: acutus - "sharp, pointed"

Definition: Ananglewhose measure is less than 90

Try this Adjust theanglebelow by dragging an orange dot and see how the angle ABC behaves. Note

that it is acute for all angles from zero to (but not including) 90

Obtuse angleFrom Latin: obtusus - "blunt"

Definition: Ananglewhose measure is greater than 90 and less than 180Try this Adjust theanglebelow by dragging the orange dot at A and see how the angle ABC behaves.

Note that it is obtuse for all angles greater than 90 and less than 180
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right angle is ananglethat bisects the angle formed by two halves

of a straight line. More precisely, if arayis placed so that its

endpoint is on a line and the adjacent angles are equal, then they

are right angles.[1]

As a rotation, a right angle corresponds to a

quarter turn (that is, a quarter of a full circle).[2]

Closely related and important geometrical concepts

areperpendicularlines, meaning lines that form right angles at their

point of intersection, andorthogonality, which is the property of

forming right angles, usually applied tovectors. The presence of a

right angle in atriangleis the defining factor forright

triangles,[3]

making the right angles basic to trigonometry.

adjacent angles, often shortened as adj. s, areanglesthathave a common ray coming out of the vertex going between two

other rays, with no overlap of the regions "enclosed" by the two

angles. In other words, they are angles that are side by side, oradjacent.

Vertical Angle a pair ofanglesis said tobe vertical (also opposite andvertically opposite, which is

abbreviated as vert. opp. s[1]) if the angles are formed from twointersectinglinesand the angles are not adjacent. The two angles

share a vertex. Such angles are equal inmeasureand can be

described as "equal" (in the UK or the USA) or "congruent" (in the

USA).
http://en.wikipedia.org/wiki/Anglehttp://en.wikipedia.org/wiki/Anglehttp://en.wikipedia.org/wiki/Line_(mathematics)#Rayhttp://en.wikipedia.org/wiki/Line_(mathematics)#Rayhttp://en.wikipedia.org/wiki/Line_(mathematics)#Rayhttp://en.wikipedia.org/wiki/Right_angle#cite_note-1http://en.wikipedia.org/wiki/Right_angle#cite_note-1http://en.wikipedia.org/wiki/Right_angle#cite_note-1http://en.wikipedia.org/wiki/Right_angle#cite_note-2http://en.wikipedia.org/wiki/Right_angle#cite_note-2http://en.wikipedia.org/wiki/Right_angle#cite_note-2http://en.wikipedia.org/wiki/Perpendicularhttp://en.wikipedia.org/wiki/Perpendicularhttp://en.wikipedia.org/wiki/Perpendicularhttp://en.wikipedia.org/wiki/Orthogonalityhttp://en.wikipedia.org/wiki/Orthogonalityhttp://en.wikipedia.org/wiki/Euclidean_vectorhttp://en.wikipedia.org/wiki/Euclidean_vectorhttp://en.wikipedia.org/wiki/Euclidean_vectorhttp://en.wikipedia.org/wiki/Trianglehttp://en.wikipedia.org/wiki/Trianglehttp://en.wikipedia.org/wiki/Trianglehttp://en.wikipedia.org/wiki/Right_trianglehttp://en.wikipedia.org/wiki/Right_trianglehttp://en.wikipedia.org/wiki/Right_trianglehttp://en.wikipedia.org/wiki/Right_angle#cite_note-3http://en.wikipedia.org/wiki/Right_angle#cite_note-3http://en.wikipedia.org/wiki/Anglehttp://en.wikipedia.org/wiki/Anglehttp://en.wikipedia.org/wiki/Anglehttp://en.wikipedia.org/wiki/Anglehttp://en.wikipedia.org/wiki/Anglehttp://en.wikipedia.org/wiki/Anglehttp://en.wikipedia.org/wiki/Vertical_angle#cite_note-tb-1http://en.wikipedia.org/wiki/Vertical_angle#cite_note-tb-1http://en.wikipedia.org/wiki/Vertical_angle#cite_note-tb-1http://en.wikipedia.org/wiki/Line_(mathematics)http://en.wikipedia.org/wiki/Line_(mathematics)http://en.wikipedia.org/wiki/Line_(mathematics)http://en.wikipedia.org/wiki/Angular_measurehttp://en.wikipedia.org/wiki/Angular_measurehttp://en.wikipedia.org/wiki/Angular_measurehttp://en.wikipedia.org/wiki/Congruence_(geometry)http://en.wikipedia.org/wiki/Congruence_(geometry)http://en.wikipedia.org/wiki/Congruence_(geometry)http://en.wikipedia.org/wiki/Congruence_(geometry)http://en.wikipedia.org/wiki/Angular_measurehttp://en.wikipedia.org/wiki/Line_(mathematics)http://en.wikipedia.org/wiki/Vertical_angle#cite_note-tb-1http://en.wikipedia.org/wiki/Anglehttp://en.wikipedia.org/wiki/Anglehttp://en.wikipedia.org/wiki/Right_angle#cite_note-3http://en.wikipedia.org/wiki/Right_trianglehttp://en.wikipedia.org/wiki/Right_trianglehttp://en.wikipedia.org/wiki/Trianglehttp://en.wikipedia.org/wiki/Euclidean_vectorhttp://en.wikipedia.org/wiki/Orthogonalityhttp://en.wikipedia.org/wiki/Perpendicularhttp://en.wikipedia.org/wiki/Right_angle#cite_note-2http://en.wikipedia.org/wiki/Right_angle#cite_note-1http://en.wikipedia.org/wiki/Line_(mathematics)#Rayhttp://en.wikipedia.org/wiki/Angle


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Complementary angles areangleswhose measures sum to

90. If the two complementary angles are adjacent (i.e. have a

commonvertexand share just one side) their non-shared

sides form aright angle.

InEuclidean geometry, the two acute angles in aright

triangleare complementary, because the sum of internal

angles of a triangle is 180 degrees, and the right angle itself

accounts for ninety degrees.

The adjective complementaryis fromLatincomplementum,

associated with the verb complere, "to fill up". An acute angle

is "filled up" by its complement to form a right angle.

Supplementary angles are pairs ofanglesthat add up to

180degrees. Thus the supplement of an angle ofxdegrees

is an angle of (180

x) degrees.

If the two supplementary angles areadjacent(i.e. have a

commonvertexand share just one side), their non-shared

sides form astraight line. However, supplementary angles do

not have to be on the same line, and can be separated in

space. For example, adjacent angles of aparallelogramare

supplementary, and opposite angles of acyclic

quadrilateral(one whose vertices all fall on a single circle)

are supplementary.

If a point P is exterior to a circle with center O, and if thetangent linesfrom P touch the circle at points T

and Q, then TPQ and TOQ are

supplementary.

Linear Pair of anglesFrom Latin: linearis - "belonging to a line"

Definition: Two angles thatareadjacent(share a leg)

andsupplementary(add up to 180)
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