السلام عليكم

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اقتبست بعض النظريات الهندسية من مواقع أجنبية

(1)
If a point is on the perpendicular bisector of a segment,
then it is equally distant from the endpoints
(Perpendicular Bisector Conjecture).



(2)
If a point is equally distant from the endpoints of a segment,
then it is on the perpendicular bisector of the segment
(Converse of the Perpendicular Bisector Conjecture).



(3)
The shortest distance from a point to a line is
measured along the perpendicular from the point to the line
(Shortest Distance Conjecture).



(4)
If a point is on the bisector of an angle,
then it is equally distant from the sides of the angle
(Angle Bisector Conjecture)



(5)
The measure of each angle of an equilateral triangle is 60°.



(6)
The three angle bisectors of a triangle are concurrent.



(7)
The three perpendicular bisectors of a triangle are concurrent.



(8)
The three altitudes (or the lines through the altitudes)
of a triangle are concurrent.



(9)
The circumcenter of a triangle is
equally distant from the triangle’s three vertices.



(10)
The incenter of a triangle is
equally distant from the triangle’s three sides.



(11)
The three medians of a triangle are concurrent.



(12)
The centroid of a triangle divides each median into two parts
so that
the distance from the centroid to the vertex is twice
the distance from the centroid to the midpoint.



(13)
The circumcenter, centroid, and the orthocenter are
the three points of concurrency that always lie on the Euler line.



(14)
The centroid divides the Euler segment into two parts
so that
the smaller part is half as long as the larger part.

 

 

15
If two angles are vertical angles, then they are congruent
(Vertical Angles Conjecture).



16
If two angles are a linear pair of angles,
then they are supplementary
(Linear Pair Conjecture).




17
If two parallel lines are cut by a transversal,
then corresponding angles are congruent,
alternate interior angles are congruent,
and alternate exterior angles are congruent
(Parallel Lines Conjecture).



17 a
If two parallel lines are cut by a transversal,
then corresponding angles are congruent
(Corresponding Angle Conjecture, or CA Conjecture).



17b
If two parallel lines are cut by a transversal,
then alternate interior angles are congruent

(Alternate Interior Angle Conjecture, or AlA Conjecture).




17 c
If two parallel lines are cut by a transversal,
then alternate exterior angles are congruent
(Alternate Exterior Angle Conjecture, or AEA Conjecture).



18
If two lines are cut by a transversal to form pairs of
congruent corresponding angles,
congruent alternate interior angles,
and congruent alternate exterior angles,
then the lines are parallel
(Converse of the Parallel Lines Conjecture).



19
If
and
are the coordinates of the endpoints of a segment,
then the coordinates of the midpoint are
,
(Coordinate Midpoint Conjecture).



20
The slope m of a line (or segment)
through P1 and P2 with coordinates (x1,y1) and (x2,y2)
where (x1 x2) is
m =
\frac{y2-y1}{x2-x1}
(Slope of a Line Conjecture).



21
In a coordinate plane, two distinct lines are parallel
if and only if their slopes are equal

(Parallel Slope Conjecture).




22
In a coordinate plane,
two nonvertical lines are perpendicular if and only if
their slopes are negative reciprocals of each other
(Perpendicular Slope Conjecture ).


23
If the graph of a line has a slope of m and
a y-intercept of (0, b ),
then the equation of the line
can be written in the form

(Slope-Intercept Conjecture).



24
If TRY has coordinates
T(a, d), R(b, e), and Y(c, f) then
the centroid has coordinates

(Centroid Coordinates Conjecture).

 

 

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السلام عليكم ورحمة الله وبركاته

جزاك الله أختنا ya_kout

أخي الكريم f-77

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