Diagonal

Definition

A diagonal is a line segment that connects two non-adjacent vertices of a polygon. It is a line that passes through the interior of the shape, dividing it into two equal parts.

5 Must Know Facts For Your Next Test

1. The diagonals of a rectangle bisect each other at right angles and are equal in length.
2. The diagonals of a parallelogram bisect each other, and the lengths of the diagonals are equal.
3. The diagonals of a rhombus are perpendicular and bisect each other at right angles.
4. In a triangle, the diagonals of a circumscribed rectangle are the sides of the triangle.
5. The diagonals of a trapezoid are not necessarily equal in length, and they do not necessarily bisect each other.

Review Questions

• Explain the relationship between the diagonals of a rectangle and their properties.
  • The diagonals of a rectangle bisect each other at right angles, meaning they intersect perpendicularly at the midpoint of each diagonal. Additionally, the diagonals of a rectangle are equal in length. These properties are a result of the rectangle's four right angles and parallel sides, which create a symmetrical shape where the diagonals divide the rectangle into four congruent triangles.
• Describe how the diagonals of a parallelogram differ from those of a rectangle.
  • While the diagonals of a rectangle bisect each other at right angles, the diagonals of a parallelogram also bisect each other, but they do not necessarily intersect at right angles. The diagonals of a parallelogram are equal in length, similar to a rectangle, but they are not necessarily perpendicular to each other. This is because a parallelogram has two pairs of parallel sides, but the angles between the sides are not all right angles, as they are in a rectangle.
• Analyze the properties of the diagonals in a trapezoid and how they differ from the diagonals of other quadrilaterals.
  • Unlike rectangles, parallelograms, and rhombi, the diagonals of a trapezoid are not necessarily equal in length, and they do not necessarily bisect each other. The diagonals of a trapezoid can have different lengths, and they may or may not intersect at right angles. This is because a trapezoid has only one pair of parallel sides, unlike the other quadrilaterals, which have two pairs of parallel sides. The asymmetry of a trapezoid's sides and angles results in diagonals that do not share the same properties as the diagonals of more regular quadrilaterals.

Related terms

Vertex:

A vertex is a point where two or more line segments meet to form a corner of a polygon.

Polygon: A polygon is a closed, two-dimensional shape made up of line segments that intersect at vertices.

Midpoint:

The midpoint of a line segment is the point that is equidistant from the two endpoints of the segment.