Midsegment and Perpendicular Bisectors

Front

What is a midsegment in a triangle?

Back

A midsegment is a line segment that connects the midpoints of two sides of a triangle. It is parallel to the third side and half its length.

Front

What is a perpendicular bisector?

Back

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

Front

How do you find the length of a midsegment?

Back

The length of a midsegment is half the length of the side of the triangle it is parallel to.

Front

What is the relationship between a perpendicular bisector and the points on it?

Back

Any point on the perpendicular bisector of a segment is equidistant from the endpoints of that segment.

Front

If line m is a perpendicular bisector of segment AB, what can be said about points A and B?

Back

Points A and B are equidistant from any point on line m.

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 equidistant from all three vertices.

Front

How do you determine if two segments are parallel?

Back

Two segments are parallel if they are in the same plane and do not intersect, or if they have the same slope.

Front

What is the significance of the circumcenter in triangle geometry?

Back

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

Front

If segment WX is parallel to segment YZ, what can be inferred about their lengths?

Back

If WX is parallel to YZ and they are part of a transversal, then the corresponding angles are equal, but their lengths may differ unless specified.

Front

What is the formula for finding the length of a segment given its endpoints?

Back

The length of a segment with endpoints (x1, y1) and (x2, y2) is given by the formula: length = √((x2 - x1)² + (y2 - y1)²).