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 its length is half the length of that side.

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

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

How do you find the length of a midsegment in a triangle?

Back

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

Front

What is the relationship between parallel lines and transversals?

Back

When a transversal crosses parallel lines, it creates corresponding angles that are equal and alternate interior angles that are also equal.

Front

If MP || DE, what can be inferred about the angles formed by a transversal?

Back

The corresponding angles and alternate interior angles formed by the transversal are equal.

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 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 of the triangle.

Front

If point G is the circumcenter, what does that imply about distances from G to the vertices of the triangle?

Back

The distances from point G to each vertex of the triangle are equal.

Front

What is the significance of the circumradius?

Back

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