3.1 Triangle Sum & Triangle Inequality

Front

What is the Triangle Sum Theorem?

Back

The Triangle Sum Theorem states that the sum of the interior angles of a triangle is always 180 degrees.

Front

What is the Triangle Inequality Theorem?

Back

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

Front

Define a median in a triangle.

Back

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

Front

What is an altitude in a triangle?

Back

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

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 circumcenter of a triangle?

Back

The circumcenter is the point where the perpendicular bisectors of the sides of a triangle intersect, and it is equidistant from the vertices.

Front

What is the incenter of a triangle?

Back

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

Front

What is the centroid of a triangle?

Back

The centroid is the point where the medians of a triangle intersect, and it is the center of mass of the triangle.

Front

How do you determine if three lengths can form a triangle?

Back

Use the Triangle Inequality Theorem: For lengths a, b, and c, check if a + b > c, a + c > b, and b + c > a.

Front

What is a perpendicular bisector?

Back

A perpendicular bisector is a line that divides a segment into two equal parts at a 90-degree angle.