Triangle Geometry: Altitudes, Medians, and Circumcenters

a. In a triangle, an altitude is shorter than either side from the same vertex.

Sometimes, right triangles are equal

b. In a triangle, an altitude is shorter than the median from the same vertex.

Sometimes ,same lengths are in a equilateral

c. In a triangle, if a perpendicular bisector of a side and an altitude coincide, then the triangle is isosceles.

Sometimes, only if drawn from vertex.

d. Exactly one altitude lies outside a triangle.

Never, if 1 is the is at least another.

e. The intersection of the perpendicular bisectors of the sides lies inside the triangle.

Sometimes, only if triangle is acute

f. The shortest distance from a point to a line is the length of the perpendicular segment from the point to the line.

Always

g. Every point on a median in a triangle is equidistant from the sides of an angle.

Sometimes, if its equillateral and therefor a angle bisec

h. The circumcenter is equidistant from all three sides of a triangle.

sometimes, if its isoceles and also an incenter

i. The centroid of a triangle divides each median into two segments so that the shorter segment is half the length of the longer segment.

Always

j. In a right triangle the circumcenter is located at the midpoint of the side opposite the right angle

Always

k. If a point is equidistant from the endpoints of a segment, then it must be the midpoint of the segment

Sometimes, the point could b e on perpendicular bisector of segment