Perpendicular and Angle Bisectors

Front

What is a perpendicular bisector?

Back

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

Front

Define angle bisector.

Back

A ray that divides an angle into two equal angles.

Front

What is the point of concurrency for perpendicular bisectors called?

Back

Circumcenter.

Front

How do you find the circumcenter of a triangle?

Back

By finding the intersection of the perpendicular bisectors of the sides of the triangle.

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

What is the formula for finding the length of a segment given its endpoints (x1, y1) and (x2, y2)?

Back

Length = √((x2 - x1)² + (y2 - y1)²).

Front

If AG = 10 and BG = x, what is the relationship between AG and BG if G is the midpoint?

Back

AG = BG, so x = 10.

Front

What is the measure of an angle if it is bisected and the original angle is 80 degrees?

Back

Each angle measures 40 degrees.

Front

What is the significance of the incenter of a triangle?

Back

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

Front

How do you determine if two lines are perpendicular?

Back

If the product of their slopes is -1.