Medians Altitudes Bisectors and Midsegments

Front

What is a median in a triangle?

Back

A median is a segment with endpoints at a vertex of the triangle and the midpoint of the opposite side.

Front

What is an altitude in a triangle?

Back

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

Front

What is a perpendicular bisector?

Back

A perpendicular bisector is a line, segment, or ray that passes through the midpoint of a side and is perpendicular to that side.

Front

What is an angle bisector?

Back

An angle bisector is a ray that divides an angle into two equal angles.

Front

If AC=42, what is DF if D is the midpoint of AC?

Back

DF = 21.

Front

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

Back

Use the formula: Median = 1/2 * sqrt(2AB^2 + 2AC^2 - BC^2), where A, B, and C are the vertices of the triangle.

Front

What is the relationship between the medians of a triangle?

Back

The three medians of a triangle intersect at a point called the centroid, which divides each median into a ratio of 2:1.

Front

What is the significance of the centroid in a triangle?

Back

The centroid is the center of mass of the triangle and is the point where the three medians intersect.

Front

If BP bisects ∠CBD and m∠2 = 7x + 5, m∠1 = 9x - 5, how do you find m∠2?

Back

Set m∠1 = m∠2, solve for x, then substitute back to find m∠2. m∠2 = 40 degrees.

Front

What is the formula for the area of a triangle using the height and base?

Back

Area = 1/2 * base * height.