Special Segments in Triangles

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 an angle bisector?

Back

An angle bisector is a line segment that divides an angle into two equal angles.

Front

What is a perpendicular bisector?

Back

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

Front

What is an altitude in a triangle?

Back

An altitude is a line segment from a vertex to the opposite side, forming a right angle with that side.

Front

How do you find the length of a median in a triangle?

Back

The length of a median can be found using the formula: m = 1/2 * √(2a² + 2b² - c²), where a and b are the lengths of the sides adjacent to the median, and c is the length of the side opposite the median.

Front

What is the relationship between the angle bisector and the sides of a triangle?

Back

The angle bisector divides the opposite side into segments that are proportional to the lengths of the other two sides.

Front

What is the significance of the centroid in relation to medians?

Back

The centroid is the point where all three medians of a triangle intersect, and it divides each median into a ratio of 2:1.

Front

How do you determine if a segment is a perpendicular bisector?

Back

A segment is a perpendicular bisector if it is perpendicular to the segment it bisects and passes through its midpoint.

Front

What is the formula for finding the area of a triangle using the altitude?

Back

The area of a triangle can be calculated using the formula: Area = 1/2 * base * height, where height is the length of the altitude.

Front

If AG = 2x + 21 and RE = x + 10.5, what is NG?

Back

NG = 26.5.