Definition

Adjective: - Having equal angles: "isogonal" describes a geometric figure or relationship where angles are equal, especially in the context of lines or curves that intersect at equal angles.

Usage Examples

• (Lines that meet at equal angles.)
• (Structures where angles are equal.)

Advanced Usage

• "isogonal line": In geometry, a line that makes equal angles with two given lines or curves.

  • The isogonal line of a triangle is the line that is symmetric to another line with respect to the angle bisector. (A line that mirrors another across the bisector.)

• "isogonal conjugate": In geometry, a transformation that maps a point to another point by reflecting lines through the angle bisectors of a triangle.

  • The isogonal conjugate of the centroid is the symmedian point. (A specific transformation in triangle geometry.)

Variants and Related Words

• Isogonic (adj): a variant spelling of "isogonal", often used in magnetism to refer to lines of equal magnetic declination.

  • Isogonic lines on a map show places with the same magnetic declination. (Lines of equal magnetic variation.)

• Isogon (n): a polygon with all angles equal.

  • A square is an isogon because all its interior angles are 90 degrees. (A shape with equal angles.)

Synonyms

• Equiangular: having equal angles (often used for polygons).
  • An equiangular triangle is also equilateral. (A triangle with equal angles.)

Related Idioms

• None common for "isogonal"; it is a technical term used primarily in mathematics and crystallography.

Note: "Isogonal" is a specialized term. In mathematics, it is most frequently used in geometry (e.g., isogonal lines, isogonal conjugates) and in crystallography to describe symmetric crystal forms.