ya_kout
07-05-2008, 10:41 PM
السلام عليكم
في منتديات الرياضيات العربية ،،،،،
اقتبست بعض النظريات الهندسية من مواقع أجنبية :d
(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.
في منتديات الرياضيات العربية ،،،،،
اقتبست بعض النظريات الهندسية من مواقع أجنبية :d
(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.