Special Segments in Triangles

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. It is equidistant from the vertices of the triangle.

Front

What is the incenter of a triangle?

Back

The incenter is the point where the angle bisectors of a triangle intersect. It is equidistant from the sides of the triangle.

Front

What is a median in a triangle?

Back

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

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. It is parallel to the third side and half its length.

Front

What is an angle bisector?

Back

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

Front

What is the relationship between the sides of a triangle?

Back

The sum of the lengths of any two sides of a triangle must be greater than the length of the third side (Triangle Inequality Theorem).

Front

How do you find the length of a side in a triangle given the other two sides?

Back

Use the Triangle Inequality Theorem to determine possible lengths, ensuring the sum of any two sides is greater than the third.

Front

What is the difference between the circumcenter and incenter?

Back

The circumcenter is equidistant from the vertices, while the incenter is equidistant from the sides of the triangle.

Front

What is the significance of the centroid in a triangle?

Back

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

Front

What is the formula for the area of a triangle?

Back

Area = 1/2 * base * height.