Medians, altitudes, angle bisectors, and perpendicular bisectors

Front

What is a median in a triangle?

Back

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

Front

What is an altitude in a triangle?

Back

An altitude is a perpendicular line segment from a vertex to the line containing 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 line segment into two equal parts at a right angle.

Front

How many medians does a triangle have?

Back

A triangle has three medians, one from each vertex.

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 * sqrt(2a^2 + 2b^2 - c^2), where a and b are the lengths of the sides adjacent to the vertex and c is the length of the opposite side.

Front

What is the relationship between the altitude and the area of a triangle?

Back

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

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

What is the difference between an altitude and a median?

Back

An altitude is perpendicular to the opposite side, while a median connects a vertex to the midpoint of the opposite side.

Front

Can an altitude be outside the triangle?

Back

Yes, in obtuse triangles, the altitude from the vertex opposite the obtuse angle falls outside the triangle.