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Angles - Coggle Diagram
Angles
Polygons
Triangle
3 angles
Congruent triangles
We say two triangles are congruent when every corresponding sides and angles are the same
Minimum requirements for two triangles to be congruent
ASA(angle, side, angle)
: Two triangles are congruent if
two angles
and
the side between
them are equal in each
SAS(side, angle, side)
: Two triangles are congruent if
two sides
and
the included angle
in each are equal
SSS(side, side, side)
: Two triangles are congruent if
all three corresponding sides
in each are equal
Theorem 2: 1. If a triangle is isosceles, then the angles opposite the equal sides are equal. 2. Conversely if angles are equal then the triangle’s sides are equal, therefore the triangle is isosceles
Quadrilateral
4 angles
Pentagon
5 angles
Hexagon
6 angles
The pairs of angles directly opposite each other are called
vertically opposite angles
Theorem 1: Vertically opposite angles are equal. <1=<3, <2=<4
Proof
: |<1+|<3|=180, |<2|+|<3|=180 =>|<1|+|<3|=|<2|+|<3| => |<1|=|<2|
Supplementary Angles
Two angles
add to 180 degrees
are called supplementary angles
Straight angle=180 degrees
d=d
|<BAC|=|<BAD|+|<BAC|
Parallel lines
: two lines that never meet
Transversal
: a line cut through two or more lines
Corresponding angles
: (equal angles)are on the
same side of the transversal
and in
corresponding position
in relation to the
parallel lines
ˇ
Interior angles
: (
two interior angles add together to 180 degrees
)must be on
same side of the transversal
and must be
inside the parallel lines
Alternate angles
: (Equal angles)on the
opposite side of the transversal
but
inside the parallel lines
Each angle has its unique point, called its
vertex
(vertices). [BA and [BC are called the
arms
of the angle. The area between the arms are called the
inside
of the angle
Types of angle
Ordinary angles: angles < 180 degrees
Right angle
= 90 degrees
90 degrees <
Obtuse angle
< 180 degrees
Acute angle
< 90 degrees
Straight angle
= 180 degrees
Reflex angle
>180 degrees
Full angle
= 360 degrees
Perpendicular lines
: two lines are at an angle 90 degrees to each other
