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 the property of perpendicular bisectors?

Back

A perpendicular bisector of a segment is a line that is perpendicular to the segment at its midpoint. Any point on the perpendicular bisector is equidistant from the endpoints of the segment.

Front

How do you find the length of a midsegment?

Back

To find the length of a midsegment, take the average of the lengths of the two sides it connects and divide by 2.

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 MN || CE, what can be inferred about the angles?

Back

If two lines are parallel, then corresponding angles formed by a transversal are equal.

Front

What is the relationship between midsegments and the sides of a triangle?

Back

Midsegments are always parallel to one side of the triangle and half its length.

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 construction?

Back

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

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).

Front

What does it mean for segments to be congruent?

Back

Segments are congruent if they have the same length.