points of concurrency-triangles

Front

What is the point of concurrency where the angle bisectors of a triangle intersect?

Back

Incenter

Tags

CCSS.HSG.C.A.3

Front

What is the point of concurrency where the perpendicular bisectors of a triangle intersect?

Back

Circumcenter

Tags

CCSS.HSG.C.A.3

Front

What is the point of concurrency where the medians of a triangle intersect?

Back

Centroid

Tags

CCSS.HSG.CO.C.10

Front

What is the point of concurrency where the altitudes of a triangle intersect?

Back

Orthocenter

Tags

CCSS.HSG.C.A.3

Front

What is the relationship between the circumcenter and the circumcircle of a triangle?

Back

The circumcenter is the center of the circumcircle, which passes through all three vertices of the triangle.

Tags

CCSS.HSG.C.A.3

Front

What is the relationship between the incenter and the incircle of a triangle?

Back

The incenter is the center of the incircle, which is tangent to all three sides of the triangle.

Tags

CCSS.HSG.C.A.3

Front

How do you find the circumcenter of a triangle using its vertices?

Back

By finding the intersection of the perpendicular bisectors of at least two sides of the triangle.

Tags

CCSS.HSG.C.A.3

Front

What is the significance of the centroid in a triangle?

Back

The centroid is the point where the three medians intersect and it divides each median into a 2:1 ratio.

Tags

CCSS.HSG.CO.C.10

Front

What is the formula for finding the coordinates of the centroid of a triangle given its vertices (x1, y1), (x2, y2), (x3, y3)?

Back

Centroid (G) = ((x1 + x2 + x3)/3, (y1 + y2 + y3)/3).

Tags

CCSS.HSG.C.A.3

Front

What is the definition of a median in a triangle?

Back

A median is a line segment that connects a vertex of the triangle to the midpoint of the opposite side.