Perpendicular Bisectors of Triangles

Front

What is a perpendicular bisector?

Back

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

Front

What is the circumcenter of a triangle?

Back

The point where the perpendicular bisectors of the sides of a triangle intersect.

Front

If CG = 4x + 3 and AG = 3x + 4, what is BG if CG = AG?

Back

BG = 7.

Front

If GC is 11, what is AG if AG = GC?

Back

AG = 11.

Front

If BC is 18 and DC is the perpendicular bisector, what is DC?

Back

DC = 9.

Front

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

Back

The circumcenter is equidistant from all three vertices of the triangle.

Front

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

Back

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

Front

What is the significance of the circumcenter in triangle geometry?

Back

It is the center of the circumcircle, the circle that passes through all three vertices of the triangle.

Front

What is the formula for finding the length of a segment if it is bisected?

Back

If a segment AB is bisected at point C, then AC = BC = 1/2 AB.

Front

What is the definition of a midsegment in a triangle?

Back

A segment that connects the midpoints of two sides of a triangle.