Special Segments in Triangles

Front

What is an altitude in a triangle?

Back

An altitude is a segment from a vertex to the line containing the opposite side, forming a right angle with that side.

Front

What is a median in a triangle?

Back

A median is a segment from a vertex to the midpoint of 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 a perpendicular bisector?

Back

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

Front

What is an angle bisector?

Back

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

Front

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

Back

Use the formula: Median = 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 opposite side.

Front

What is the relationship between the altitude and the area of a triangle?

Back

The area of a triangle can be calculated using the formula: Area = 1/2 * base * height (where height is the length of the altitude).

Front

How do you determine if a segment is an altitude?

Back

Check if the segment forms a right angle with the opposite side of the triangle.

Front

What is the significance of the centroid in relation to medians?

Back

The centroid is the point where all three medians of a triangle intersect, and it divides each median into a ratio of 2:1.

Front

How can you identify a midsegment in a triangle?

Back

A midsegment connects the midpoints of two sides and is parallel to the third side, and its length is half the length of that side.