Segments in triangles

Front

What is a median in a triangle?

Back

A segment with endpoints at the vertex and midpoint of the opposite side.

Front

What is a midsegment in a triangle?

Back

A segment that connects the midpoints of two sides of a triangle.

Front

What is an angle bisector?

Back

A segment that divides an angle into two equal angles.

Front

What is a perpendicular bisector?

Back

A segment that is perpendicular to a side of a triangle at its midpoint.

Front

Given segment AM is a median in ΔABC. Find the length of segment BC if AM = 17.

Back

34

Front

If a triangle has sides of lengths 6, 8, and 10, which segment is the median to the longest side?

Back

The median to the side of length 10.

Front

What is the relationship between the lengths of the medians in a triangle?

Back

The length of a median is always less than the length of the side it bisects.

Front

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

Back

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

Front

If a triangle has vertices at (0,0), (4,0), and (2,3), what is the length of the median from (2,3) to the midpoint of the base?

Back

The length of the median is 2.5.

Front

What is the formula for finding the length of a median in a triangle?

Back

Length of median = √(2a² + 2b² - c²) / 4, where a and b are the lengths of the sides adjacent to the median and c is the length of the side opposite the median.