Chapter 5

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

What is a triangle's range of possible side lengths?

Back

For any triangle with sides of lengths a, b, and c, the lengths must satisfy the inequalities: a + b > c, a + c > b, and b + c > a.

Front

Define an angle bisector in a triangle.

Back

An angle bisector is a line segment that divides an angle into two equal angles and extends from the vertex to the opposite side.

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.

Front

Can a triangle have sides of lengths 3, 4, and 9? Why or why not?

Back

No, because the sum of the lengths of the two shorter sides (3 + 4 = 7) is not greater than the length of the longest side (9). This violates the Triangle Inequality Theorem.

Front

What is the definition of a triangle?

Back

A triangle is a polygon with three edges and three vertices.

Front

What are the types of triangles based on side lengths?

Back

Triangles can be classified as equilateral (all sides equal), isosceles (two sides equal), or scalene (all sides different).

Front

What are the types of triangles based on angles?

Back

Triangles can be classified as acute (all angles less than 90°), right (one angle equal to 90°), or obtuse (one angle greater than 90°).

Front

What is the significance of the centroid in a triangle?

Back

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

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.