Midsegment / 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.

Front

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

Back

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

Front

Define perpendicular bisector.

Back

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

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.

Front

How is the circumcenter related to the vertices of a triangle?

Back

The circumcenter is equidistant from each vertex of the triangle.

Front

What is the significance of the midsegment in triangle WUV if QR is a midsegment?

Back

QR is parallel to side UV and its length is half the length of side UV.

Front

If the length of side UV is 16, what is the length of midsegment QR?

Back

QR = 8 (half of 16).

Front

What is the difference between a median and a midsegment?

Back

A median connects a vertex to the midpoint of the opposite side, while a midsegment connects the midpoints of two sides.

Front

What is the altitude of a triangle?

Back

An altitude is a perpendicular segment from a vertex to the line containing the opposite side.

Front

If a triangle has sides of lengths 10, 12, and 14, what is the length of the midsegment connecting the sides of lengths 10 and 12?

Back

The length of the midsegment is 7 (half of the length of the third side, which is 14).