Triangle Properties and Segments

The video tutorial covers key geometric concepts related to triangles, including medians, centroids, altitudes, angle bisectors, and perpendicular bisectors. It explains how medians connect a vertex to the midpoint of the opposite side, forming centroids where they intersect. Altitudes are described as lines from a vertex perpendicular to the opposite side, representing the triangle's height. Angle bisectors divide angles into two equal parts, while perpendicular bisectors are lines that bisect a side at a right angle, equidistant from the vertices.

What is the definition of a median in a triangle?

• A line segment from a vertex to the opposite vertex

• A line segment from a vertex to the midpoint of the opposite side

• A line segment that is perpendicular to a side

• A line segment that bisects an angle

Where do all the medians of a triangle meet?

• At the orthocenter

• At the centroid

• At the circumcenter

• At the incenter

What is the ratio of the segments created by the centroid on a median?

• 2:3

• 1:1

• 1:2

• 2:1

What is an altitude in a triangle?

• A line segment from a vertex to the midpoint of the opposite side

• A line segment that is parallel to a side

• A line segment from a vertex perpendicular to the opposite side

• A line segment that bisects an angle

In a right triangle, where is one of the altitudes located?

• On the hypotenuse

• On the base

• Outside the triangle

• Inside the triangle

What is an angle bisector in a triangle?

• A line segment that divides an angle into two equal parts

• A line segment that is parallel to a side

• A line segment that is perpendicular to a side

• A line segment from a vertex to the midpoint of the opposite side

What is a perpendicular bisector in a triangle?

• A line segment that bisects an angle

• A line segment from a vertex to the midpoint of the opposite side

• A line segment that is parallel to a side

• A line segment that divides a side into two equal parts and is perpendicular to it

Does a perpendicular bisector always pass through a vertex?

• Only in right triangles

• Only in equilateral triangles

• No, not necessarily

• Yes, always

What is the unique property of points on a perpendicular bisector?

• They are equidistant from the endpoints of the segment it bisects

• They are equidistant from the vertices of the triangle

• They are equidistant from the incenter

• They are equidistant from the centroid