Which of the following describes a median of a triangle?
(1 point)
• a segment drawn from a vertex to the midpoint of the opposite side
• a segment drawn from the vertex perpendicular to the line containing the opposite side
O a segment drawn through the midpoint of a side and at a right angle to the side.
• a segment drawn from the center of an angle to the side opposite.
The correct answer is:
• a segment drawn from a vertex to the midpoint of the opposite side.
To understand why this is the correct answer, let's break down the options:
Option 1: "a segment drawn from a vertex to the midpoint of the opposite side." This describes a median of a triangle accurately. A median is a line segment that connects a vertex of a triangle to the midpoint of the side opposite to that vertex. It is worth noting that every triangle has three medians.
Option 2: "a segment drawn from the vertex perpendicular to the line containing the opposite side." This describes a perpendicular bisector, not a median. A perpendicular bisector is a line segment that passes through a vertex and is perpendicular to the opposite side.
Option 3: "a segment drawn through the midpoint of a side and at a right angle to the side." This describes a perpendicular bisector as well. While it's true that a median passes through the midpoint of a side, it does not necessarily need to be at a right angle to the side.
Option 4: "a segment drawn from the center of an angle to the side opposite." This describes an angle bisector, not a median. An angle bisector is a line segment that divides an angle into two congruent angles, and it does not necessarily pass through the midpoint of a side.
Therefore, the correct answer is option 1, which describes a median of a triangle as a segment drawn from a vertex to the midpoint of the opposite side.