Points of Concurrency - Bisectors, Medians, Altitudes

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Median

The line segment joining a vertex to the midpoint of the opposite side is the ___.

perpendicular bisector

The line segment that is both perpendicular to a side of a triangle and passes through its midpoint is the ___.

Angle Bisector

The segment drawn from a vertex that bisects that angle is the ___.

Altitude

The segment that makes a right angle and goes through the vertex is the ___.

Orthocenter

The three altitudes of a triangle intersect at the

Incenter

The three angle bisectors of a triangle intersect at the

Centroid

The three medians of a triangle intersect at the

Circumcenter

The three perpendicular bisectors of a triangle intersect at the

Incenter

The triangle center shown is the ___.

Circumcenter

Which point of concurrency is located on the hypotenuse of a right triangle?

Orthocenter

Which point of concurrency is located on the right angle of a right triangle?

Centroid

Which point of concurrency is shown?

Circumcenter

Which point of concurrency is shown?

Orthocenter

Which point of concurrency is shown?

Incenter

Which point of concurrency is shown?.

Orthocenter and Circumcenter

Which two points of concurrency are always located outside of an obtuse triangle?

never

(Always/sometimes/never?) The incenter is _______ outside the triangle

sometimes

(Always/sometimes/never?) The median of a triangle is _______ the same as the angle bisector

never... (only in an isosceles or equilateral triangle)

(always/sometimes/never?) In a scalene triangle, the angle bisector is also the median

always

(always/sometimes/never?) In an equilateral triangle, the centroid is also the circumcenter.

20

If a median has a length of 30, how long is the segment from vertex to centroid? (the big piece)

12

If the big piece of the median (vertex to centroid) is 24, how long is the small piece (centroid to side)?

Altitude

Is a median, altitude, angle bisector, or perpendicular bisector shown?

Angle Bisector

Is a median, altitude, angle bisector, or perpendicular bisector shown?

Median

Is a median, altitude, angle bisector, or perpendicular bisector shown?

Perpendicular Bisector

Is a median, altitude, angle bisector, or perpendicular bisector shown?

Centroid

It divides each median into two sections at a 2:1 ratio.

Incenter

It is equidistant from the three sides of a triangle.

Circumcenter

It is equidistant from the three vertices of a triangle.


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