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What area of a triangle does a perpendicular bisector split?
a line that intersects an edge of a triangle that is perpendicular to it and passes through the midpoint
An altitude of a triangle is a line or segment that passes through a vertex of the triangle and is?
and is perpendicular to the opposite side.
What is a segment that passes through of vertex and is perpendicular to the opposite side?
The segment that passes through a vertex and is perpendicular to the opposite side is called the altitude of the triangle.
An altitude of a triangle is a line or segment that passes through a vertex of the triangle and is to the line containing the opposite side?
perpendicular
An altitude of a triangle is a line or segment that passes through a vertex of the triangle and is perpendicular to the line containing the opposite?
side
An of a triangle is a line segment that passes through the vertex of the triangle and is perpendicular to the lines containing the opposite side?
Altitude.
Does a perpendicular bisector of a triangle always passes through the opposite vertex?
No, the perpendicular bisector of a side of a triangle does not necessarily pass through the opposite vertex. The perpendicular bisector is a line that is perpendicular to a segment at its midpoint, and it may intersect the interior or exterior of the triangle, depending on its shape. In fact, the only time a perpendicular bisector passes through the opposite vertex is in the case of an isosceles triangle, where the two sides are equal, and their perpendicular bisectors coincide with the altitude.
A median of a triangle is a line or segment that passes through a vertex and the side opposite that vertex?
A median of a triangle is a line or segment that passes through a vertex and the midpoint of the side opposite that vertex. The median only bisects the vertex angle from which it is drawn when it is an isosceles triangle.
What passes through a triangle through the midpoint of side ofa triangle and is perpendicular to that side of the triangle?
Those would be perpendicular bisectors. If you do that to each side of the triangle they all meet at what is called the circumcenter. http://mathworld.wolfram.com/Circumcircle.html
What are perpendicular bisectors?
A line that is perpendicular to the segment of a plane and passes through the midpoint.
Why does a line segment have one midpoint and can have many bisectors?
A bisector is a line (or line segment) which passes through the midpoint. You can have multiple lines intersect at this one point, and all of them will bisect the original line segment, since they pass through its midpoint. A perpendicular bisector passes through the midpoint, and also is perpendicular to the original line segment, so there will be only one of those.
What if the altitude to the hypotenuse of a right triangle is the geometric mean between the segments on the hypotenuse?
Always true. To see this draw the circle which passes through the three points of the triangle. Reproduce the reflection of the triangle on the hypotenuse (which passes through the centre). Then use the theorem of intersecting chords of a circle to give the result immediately. It's also simply proved by algebra.
