Centers of Triangles

Front

What is the Incenter of a triangle?

Back

The Incenter is the point where the angle bisectors of a triangle intersect. It is equidistant from all three sides of the triangle.

Tags

CCSS.HSG.C.A.3

Front

What is the Circumcenter of a triangle?

Back

The Circumcenter is the point where the perpendicular bisectors of the sides of a triangle intersect. It is the center of the circumcircle, which passes through all three vertices.

Tags

CCSS.HSG.C.A.3

Front

What is 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.

Front

What is the Centroid of a triangle?

Back

The Centroid is the point where the three medians of a triangle intersect. It is also the center of mass of the triangle.

Tags

CCSS.HSG.CO.C.10

Front

What is a perpendicular bisector?

Back

A perpendicular bisector is a line that divides a segment into two equal parts at a 90-degree angle.

Front

If CF, BE, and AD are the medians of triangle ABC, what is the relationship between the segments?

Back

The Centroid divides each median into two segments, with the longer segment being twice the length of the shorter segment.

Tags

CCSS.HSG.CO.C.10

Front

How do you find the length of a segment when given a median?

Back

To find the length of a segment when given a median, use the property that the median divides the opposite side into two equal segments.

Tags

CCSS.HSG.CO.C.10

Front

What is the relationship between the angles formed by the Incenter?

Back

The angles formed by the Incenter are equal to half the measure of the angles of the triangle.

Tags

CCSS.HSG.C.A.3

Front

What is the formula for finding the area of a triangle using the Inradius?

Back

Area = r * s, where r is the Inradius and s is the semi-perimeter of the triangle.

Tags

CCSS.HSG.SRT.D.9

Front

What is the semi-perimeter of a triangle?

Back

The semi-perimeter (s) is half the sum of the lengths of the sides of the triangle: s = (a + b + c) / 2.

Tags

CCSS.4.MD.A.3