Segments in triangles

Front

What is a median in a triangle?

Back

A median is a line segment that connects a vertex of a triangle to the midpoint of the opposite side.

Front

What is an altitude in a triangle?

Back

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

Front

What is a midsegment in a triangle?

Back

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

Front

What is an angle bisector in a triangle?

Back

An angle bisector is a line that divides an angle into two equal parts.

Front

If AC = 42, what is the length of DF if DF is a midsegment?

Back

DF = 21 (DF is half the length of AC).

Front

In triangle ABC, if AM is a median, what can be said about segments BM and MC?

Back

BM = MC (the median divides the opposite side into two equal segments).

Front

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

Back

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

Front

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

Back

The length of the median to the longest side (10) is 7.5.

Front

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

Back

The length of a median can be calculated using the formula: m = 1/2 * sqrt(2a^2 + 2b^2 - c^2), 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.

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.