Question

do you understand?

1. essential question what are the properties of the medians in a triangle? what are the properties of the altitudes in a triangle?

Explanation:

A median of a triangle is a line segment joining a vertex to the midpoint of the opposite side. The three medians of a triangle intersect at a single point called the centroid. The centroid divides each median into a ratio of 2:1, with the longer segment being closer to the vertex.

An altitude of a triangle is a perpendicular segment from a vertex to the line containing the opposite side (or its extension). In an acute triangle, all altitudes lie inside the triangle. In a right triangle, the two legs are altitudes, and the third altitude lies inside the triangle. In an obtuse triangle, two altitudes lie outside the triangle. The three altitudes of a triangle intersect at a single point called the orthocenter.

Answer:

• Properties of medians: A median connects a vertex to the mid - point of the opposite side. The medians of a triangle are concurrent (intersect at one point called the centroid), and the centroid divides each median in a ratio of \(2:1\) (vertex to centroid : centroid to mid - point).
• Properties of altitudes: An altitude is a perpendicular segment from a vertex to the line containing the opposite side (or its extension). The altitudes of a triangle are concurrent (intersect at one point called the orthocenter). The position of the orthocenter depends on the type of triangle (inside for acute, at the right - angle vertex for right, outside for obtuse).