U3C2: Special Segments in Triangles

Question 1

concurrent

Answer 1

concurrent segments are three or more segments that intersect at a single point

Question 2

altitude

Answer 2

the line that passes through a vertex of a triangle and is perpendicular to the opposite side

Question 3

median

Answer 3

a segment whose endpoints are the vertex of a triangle and the midpoint of the opposite side

Question 4

angle bisector

Answer 4

a line that passes through a vertex and divides the angle into two congruent angles

Question 5

perpendicular bisector

Answer 5

the line that passed through the midpoint of a side of a triangle and is perpendicular to that side

Question 6

orthocenter

Answer 6

the point of concurrency of the altitudes of a triangle

location changes based on type of triangle

Question 7

centroid

Answer 7

the point of concurrency of the medians of a triangle

Question 8

incenter

Answer 8

the point of concurrency of the angle bisectors of a triangle

a circle can be drawn inside the triangle with the incenter as its center

Question 9

circumcenter

Answer 9

the point of concurrency of the perpendicular bisectors of a triangle

location changes based on type of triangle - on right triangle, will be located on hypotenuse
a circle can be drawn outside of the triangle with the circumcenter as its center

Question 10

what do you know about the centroid of any triangle?

Answer 10

it cuts each median into two parts with a ratio of 1:2, with the longer segment being closer to the vertex. this means that the part of the median closer to the vertex is twice as long as the part of the median closer to the midpoint.

Question 11

what do you know about the incenter’s distance from each side of a triangle?

Answer 11

same distance

Question 12

what do you know about the circumcenter’s distance from each vertex of a triangle?

Answer 12

same distance