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, and it is parallel to the third side.

Front

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

Back

The length of a midsegment is half the length of the third side.

Front

What is a perpendicular bisector?

Back

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

Front

How do you find the circumcenter of a triangle?

Back

The circumcenter is found by constructing the perpendicular bisectors of at least two sides of the triangle; the point where they intersect is the circumcenter.

Front

If MP || DE, what can be inferred about the segments?

Back

If MP is parallel to DE, then the corresponding angles formed with a transversal are equal.

Front

What is the significance of the circumcenter in a triangle?

Back

The circumcenter is equidistant from all three vertices of the triangle, making it the center of the circumcircle.

Front

If G is the circumcenter and FC = 24, what does this imply about the triangle?

Back

It implies that the distance from the circumcenter G to vertex F is 24 units.

Front

What is the relationship between parallel segments in a triangle?

Back

Parallel segments in a triangle maintain equal corresponding angles and proportional lengths.

Front

How do you determine the length of a missing segment in a triangle?

Back

You can use properties of similar triangles, the Pythagorean theorem, or the midsegment theorem to find the missing length.

Front

If the midsegment MN is parallel to side HI, what can be said about their lengths?

Back

The length of MN is half the length of HI.