Special Segments Flashcards
(18 cards)
Match the Special Segments with their according pair:
Angle BIsectors Orthocenter
Perpendicular Bisectors Incenter
Altitudes Centroid
Medians Circumcenter
Angle Bisectors; Incenter
Perpendicular Bisectors; Circumcenter
Altitudes; Orthocenter
Medians; Centroid
What is the centroid of a triangle?
The centroid is the point where the three medians of the triangle intersect.
True or False: The centroid divides each median in a ratio of 2:1.
True
What is the ratio of the lengths of the segments formed by the centroid on a median?
The ratio is 2:1, with the longer segment being closer to the vertex.
What is the circumcenter of a triangle?
The circumcenter is the point where the three perpendicular bisectors of the sides intersect.
True or False: The circumcenter is always located inside the triangle.
False
What is the orthocenter of a triangle?
The orthocenter is the point where the three altitudes of the triangle intersect.
True or False: The orthocenter is always located inside the triangle.
False
What is the incenter of a triangle?
The incenter is the point where the angle bisectors of the triangle intersect.
True or False: The incenter is always located inside the triangle.
True
What is the relationship between the incenter and the sides of the triangle?
The incenter is equidistant from all three sides of the triangle.
What segment connects the incenter to the sides of the triangle?
The segment is called the ‘distance from the incenter to the side’ or simply the ‘inradius’ (not to be mentioned).
What is a median in a triangle?
A median is a line segment joining a vertex to the midpoint of the opposite side.
What is the ratio of the lengths of the segments formed by the centroid on a median?
The ratio is 2:1, with the centroid dividing the median.
What is a perpendicular bisector?
A perpendicular bisector is a line that divides a segment into two equal parts at a right angle.
What is the relationship between the circumcenter and the sides of the triangle?
The circumcenter is equidistant from all three vertices of the triangle.
What is an altitude in a triangle?
An altitude is a perpendicular segment from a vertex to the line containing the opposite side.
Fill in the blank: The median of a triangle connects a vertex to the ________ of the opposite side.
midpoint
