Special segments, points of concurrency, and special properties

Front

What is a median in a triangle?

Back

A median is a line segment that connects a vertex of a triangle to the midpoint of the opposite side.

Front

What is the definition of a perpendicular bisector?

Back

A perpendicular bisector is a line that divides a segment into two equal parts at a 90-degree angle.

Front

If a line is perpendicular to another line, what can be said about their angles?

Back

They intersect to form right angles (90 degrees).

Front

What is the relationship between the segments created by a median in a triangle?

Back

The median divides the triangle into two segments that are equal in length.

Front

If AD = 12 and AG is a segment of AD, what is AG if G is the midpoint of AD?

Back

AG = 6.

Front

What is the definition of an altitude in a triangle?

Back

An altitude is a perpendicular segment from a vertex to the line containing the opposite side.

Front

What is the significance of points of concurrency in triangles?

Back

Points of concurrency are points where three or more lines intersect, such as the centroid, orthocenter, and circumcenter.

Front

What is the centroid of a triangle?

Back

The centroid is the point where the three medians of a triangle intersect, and it is also the center of mass.

Front

What is the circumcenter of a triangle?

Back

The circumcenter is the point where the perpendicular bisectors of the sides of a triangle intersect, and it is the center of the circumscribed circle.

Front

What is the orthocenter of a triangle?

Back

The orthocenter is the point where the altitudes of a triangle intersect.