Is a segment from a vertex to the line containing the opposite side and perpendicular to the line containing that side?

An altitude of the triangle is the line segment from a vertex to the opposite side and perpendicular to the opposite side. The orthocenter will not always be inside the triangle. This is why the orthocenter is the point of concurrency of the lines containing the altitudes rather than just the altitudes.

What is a segment that runs from the vertex of a triangle and divides the opposite side into two congruent parts?

In geometry, a median of a triangle is a line segment joining a vertex to the midpoint of the opposite side, thus bisecting that side.

What is a segment from a vertex to the opposite side?

Every triangle has three bases and three altitudes (or heights). Every altitude is the perpendicular segment from a vertex to its opposite side (or the extension of the opposite side). Some altitudes overlap with a side of the triangle or meet an extended base outside the triangle.

Which segments are perpendicular to a side of a triangle?

A perpendicular bisector is a line (or segment or ray) that is perpendicular to a side of the triangle and also bisects that side of the triangle by intersecting the side at its midpoint. The perpendicular bisector may, or may NOT, pass through the vertex of the triangle.

Is a perpendicular line segment drawn from the vertex of a triangle to the opposite side?

The altitude of a triangle is the perpendicular line segment drawn from the vertex of the triangle to the side opposite to it. It is also known as the height or the perpendicular of the triangle.

What would you call a triangle where all three sides are congruent?

Equilateral triangle
Equilateral triangle: A triangle with three congruent sides.

What cuts an angle into two congruent parts?

An angle bisector is a ray that divides an angle into two congruent angles, each having a measure exactly half of the original angle. Every angle has exactly one angle bisector.