Term
|
Definition
A,B,C,D
s.t.
any 2 segments have
endpoint
or
no common vertices |
|
|
Term
|
Definition
ABCD s.t.
each vertex is contained in angle |
|
|
Term
|
Definition
Quad ABCD s.t.
AB // CD
AD // BC
|
|
|
Term
|
Definition
A quad ABCD s.t. either
AB // CD
BC //AD |
|
|
Term
|
Definition
| A quad s.t. all four angles are congruent |
|
|
Term
|
Definition
| A quad s.t. all four sides are congruent |
|
|
Term
|
Definition
| A rhombus and a Rectangle |
|
|
Term
|
Definition
| Same shape but different size |
|
|
Term
|
Definition
| A segment joining a vertex of a triangle and the midpoint of the opposite side |
|
|
Term
|
Definition
| A line through one vertex that is perpendicular to the line determined by the other two vertices |
|
|
Term
|
Definition
| The point of concurrency of the three medians |
|
|
Term
| CircumCenter of a Triangle |
|
Definition
| Intersection of the perpendicular bisectors of the sides |
|
|
Term
|
Definition
| Intersection of the three altitudes |
|
|
Term
|
Definition
| Intersection of the three angle bisectors of a triangle |
|
|
Term
|
Definition
| Intersection of the interiors of the three angles |
|
|
Term
|
Definition
|
|
Term
|
Definition
Decomposition of a polygonal region into triangles
s.t.
the conditions of polygonal regions hold |
|
|
Term
|
Definition
Given two regions, R, R' with
a(R) = a(R')
find Trianglulations T, T'
that shows R = R' |
|
|
Term
|
Definition
A circle that contains all
three vertices of a triangle |
|
|
Term
|
Definition
| A circle inscribed inside the triangle |
|
|
Term
|
Definition
| Circles that are tangent to one side of a triangle |
|
|
Term
|
Definition
Circle containing:
Midpoints
Feet of the Altitudes
Midpoints of the segments joining the orthocenter to the three vertices |
|
|
Term
| Converse of the Alternate Interior Angles Theorem |
|
Definition
If two parallel lines are cut by a transversal
then both pairs of alternate interior angles are congruent |
|
|
Term
|
Definition
If l and l' are cut by a transversal s.t.
the sum of 2 interior angles on the same side of t is less than 180, then l and l' intersect at that side of t |
|
|
Term
|
Definition
| If l and l' are parallel lines and t not equal to l is a line s.t. t intersects l then t intersects l' |
|
|
Term
| Transitivity of Parallelism |
|
Definition
If l // m
and l // n
then m //n |
|
|
Term
|
Definition
| The sum of the angles in a triangle is 180 |
|
|
Term
|
Definition
|
|
Term
|
Definition
| If ABC is a triangle and DE is a segment then there exists a point F s.t. ABC ~ DEF |
|
|
Term
| Parallel Projection Theorem |
|
Definition
3 parallels cut by 2 transversals
are proportional |
|
|
Term
| Fundamental Theorem of Similar Triangles |
|
Definition
IF ABC ~ DEF then
AB/AC = DE / DF |
|
|
Term
|
Definition
| The three medians of any triangle are concurrent |
|
|
Term
|
Definition
The orthocenter, circumcenter, and centroid of a triangle are collinear s.t.
H*G*O |
|
|
Term
|
Definition
Let t be a line, C(O, r) be a circle
and P be a point s.t P is in T&Y
The line t is tangent to the circle C at P iff
OP perp t |
|
|
Term
|
Definition
| C is a circle, l is a secant line that intersects C at two points P and Q then O lies on the perp bisector of the chord PQ |
|
|
Term
|
Definition
Every Triangle has a unique inscribed circle.
The bisectors of the interior angles are concurrent and the point of concurrency is the incenter of the triangle |
|
|
Term
|
Definition
| The measure of an inscribed angle for a circle is one half the measure of the corresponding central angle |
|
|
Term
|
Definition
| If two inscribed angles intercept the same arc, then the angles are congruent |
|
|
Term
| Nine Point Circle Theorem |
|
Definition
If
ABC is a Triangle
Then there exists a circle with:
Midpoints of ABC, feet of the altitudes of ABC, and midpoitns of segments joining orthocenter and vertices
|
|
|
Term
|
Definition
The nine-point circle is tangent to each
of the four equicircles |
|
|
Term
|
Definition
|
|
Term
|
Definition
|
|
Term
| Fundamental Theorem of Dissection Theory |
|
Definition
If R and R' are two polygonal regions
s.t. a(R) = a(R') then R = R' |
|
|
