Here are 8 very important terms for this unit, with pictures to help you understand the term better.
Term 1: Angle Bisector- a ray or line that cuts an angle into two congruent angles
Symbol: No symbol
Term 1: Angle Bisector- a ray or line that cuts an angle into two congruent angles
Symbol: No symbol
Statement: Ray MO is an angle bisector of Angle VMS, because Angles VMO and OMS are congruent.
Reason Chosen: Angle bisectors are very important to know when one starts learning about the different centers of triangles, specifically the incenter.
Term 2: Perpendicular Bisector- a ray, line, or line segment that cuts a line segment into two congruent parts
Symbol: No symbol
Term 2: Perpendicular Bisector- a ray, line, or line segment that cuts a line segment into two congruent parts
Symbol: No symbol
Statement: Line segment OR is a perpendicular bisector of Line segment VS, because segments VM and MS are congruent.
Reason Chosen: Perpendicular bisectors are very important to know when one starts learning about the different centers of a triangle, specifically the circumcenter.
Term 3: Median- a ray, line, or line segment that passes through the vertex of a triangle and the midpoint of the opposite side
Symbol: No symbol
Term 3: Median- a ray, line, or line segment that passes through the vertex of a triangle and the midpoint of the opposite side
Symbol: No symbol
Statement: Line segment VO is a median of Triangle VMS, because segments MO and OS are congruent and it passes through Point V.
Reason Chosen: Medians are very important to know when one starts learning about the different centers of a triangle, specifically the centroid.
Term 4: Altitude- a ray, line, or line segment that passes through the vertex of a triangle and is perpendicular with the opposite side
Symbol: No symbol
Term 4: Altitude- a ray, line, or line segment that passes through the vertex of a triangle and is perpendicular with the opposite side
Symbol: No symbol
Statement: Line VO is an altitude of Triangle VMS, because it passes through Point V and makes a right angle with Line segment MS.
Reason Chosen: Altitudes are very important to know when one starts learning about the different centers of a triangle, specifically the orthocenter.
Term 5: Incenter- the point where all three angle bisectors of a triangle's angles intersect
Symbol: No symbol
Term 5: Incenter- the point where all three angle bisectors of a triangle's angles intersect
Symbol: No symbol
Statement: Point O is the incenter of Triangle VMS, because all three angle bisectors of the triangle (segments MO, VO, and SO) meet there.
Reason Chosen: The incenter is the center of the inscribed circle of a triangle, which is very important to know in other applications of geometry.
Term 6: Circumcenter- the point where all three perpendicular bisectors of a triangle's sides intersect
Symbol: No symbol
Term 6: Circumcenter- the point where all three perpendicular bisectors of a triangle's sides intersect
Symbol: No symbol
Statement: Point O is the circumcenter of Triangle VMS, because all three of the triangle's perpendicular bisectors meet there.
Reason Chosen: The circumcenter is the center of the circumscribed circle of a triangle, which is very important to know in other applications of geometry.
Term 7: Centroid- the point where all three of a triangle's medians intersect
Symbol: No symbol
Term 7: Centroid- the point where all three of a triangle's medians intersect
Symbol: No symbol
Statement: Point O is the centroid of Triangle VMS, because all three of the triangle's medians meet there.
Reason Chosen: The centroid of a triangle is also its point of balance, or center of gravity. This means that, if held up on that exact point, the triangle would stay there and not fall.
Term 8: Orthocenter- the point where all three of a triangle's altitudes intersect
Symbol: No symbol
Term 8: Orthocenter- the point where all three of a triangle's altitudes intersect
Symbol: No symbol
Statement: Point O is the orthocenter of Triangle VMS, because all three of the triangle's altitudes meet there.
Reason Chosen: The orthocenter of a triangle lies on the triangle's Euler Line, along with the triangle's circumcenter and centroid. Also, if the orthocenter is inside the triangle, the triangle is acute; if the orthocenter is on the triangle, it is a right triangle; if the orthocenter is outside the triangle, the triangle is obtuse. So, the orthocenter can help one discover what type of triangle they are looking at.