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The Geometry Dictionary

Geometry is the study of shape, size, and configurations. The common types of geometry are: solid geometry, plane geometry, and spherical geometry. Today, geometry is used in the study of astronomy, chemistry, and other sciences.

Line and Segments

Parallel Lines: Infinite lines in a plane that do not meet or intersect are called parallel lines. The symbolic representation for parallel is ||.

Perpendicular Lines: The lines that intersect at right angle or intersect at 90° are called perpendicular lines. The symbol for perpendicular is.

Perpendicular Bisector: The perpendicular bisector of a line segment is the perpendicular line that passes through the midpoint of the line segment.

Bisector of a Segment: The bisector of a segment is a ray, line, plane, or segment that intersects or meets the segment at its midpoint.

Angles

Angle Bisector: The angle bisector is the ray that bisects the angle into two congruent angles.

Complementary Angles: The complementary angles are a pair of angles whose measures add up to 90°.

Acute Angle: An acute angle is the positive angle with measure between 0° and 90° or less than 90°.

Obtuse Angle: An obtuse angle is an angle with measure between 90° and 180°.

Right Angle: A right angle is an angle with measure 90°.

Reflex Angle: A reflex angle is an angle with measure between 180° and 360°.

Supplementary Angles: The supplementary angles are a pair of angles whose measures add up to 180°.

Alternate Interior Angles: The alternate interior angles are pair of angles which are on alternate sides of the transversal and inside the parallel lines.

Corresponding Angles: The corresponding angles are a pair of angles that are in the same relative position but on the other line.

Vertical Angles: Vertical angles are a pair of nonadjacent angles with equal measures, formed when two lines intersect.

Congruent Angles: Congruent angles are a pair of angles with equal measures.

Triangles

Equilateral Triangle: A triangle is equilateral if all the three sides are equal.

30-60-90 Triangle: In 30-60-90 triangle, the three angles are in the ratio 1:2:3 and the hypotenuse length is twice the length of the shorter leg.

45-45-90 Triangle: In 45-45-90 triangle, the angles are in the ratio 1:1:2 and the hypotenuse length is the square root of two times the length of either of the legs.

3-4-5 Triangle: The 3-4-5 triangle is a right triangle whose sides are in the ratio of 3:4:5.

Isosceles Triangle: In isosceles triangle, the two sides are equal.

Scalene Triangle: A scalene triangle is a triangle without congruent sides and congruent angles.

Acute Triangle: In acute triangle all three angles are acute with measure less than 90°.

Obtuse Triangle: An obtuse triangle has one angle more than 90°.

Right Isosceles Triangle: A right isosceles triangle is a right triangle with two equal sides.

Median: The median of a triangle is a line segment that joins the vertex of the triangle with the midpoint of the opposite side.

Altitude: An altitude of a triangle is a perpendicular segment drawn through a vertex to the opposite side of the triangle.

Perpendicular Bisector of Side: The perpendicular bisector of the side is a line segment that divides a side of a triangle at right angle.

Incenter, Inscribed Circle: The inscribed circle is the circle that touches the three sides of a triangle and the incenter is the center of the inscribed circle.

Balance point: The balance point or centroid of a triangle is the center point of a triangle and it is known as the triangle’s center of gravity.

Circumcenter, Circumscribed Circle: A circumscribed circle is a circle that has all the three vertices of a triangle and the center of the circumscribed circle is the circumcenter.

Right Triangle, hypotenuse, legs: A right triangle has one right angle, hypotenuse is the side opposite to the right angle and the other two sides are called legs.

Quadrilaterals

Quadrilateral: A quadrilateral is a four sided polygon.

Rhombus: A rhombus is a quadrilateral whose all four sides have equal length.

Trapezoid: A trapezoid is a four sided figure with a pair of parallel sides.

Parallelogram: A parallelogram is a quadrilateral with two pairs of parallel sides. 

Square: A square is a parallelogram with four equal angles and equal sides.

Rectangle: A rectangle is a parallelogram with four right angles.

Kite: A kite is a four sided polygon with two equal pairs of adjacent sides.

Isosceles Trapezoid: A trapezoid with a pair of parallel sides and equal base angles are called isosceles trapezoid.

Inscribed Quadrilateral: An inscribed quadrilateral (cyclic quadrilateral), is a quadrilateral inscribed inside a circle with the opposite angles being supplementary.

Opposite Sides: In a quadrilateral ABCD, the sides AB and CD are called opposite sides.

Diagonal: The diagonal is a line segment that connects two non-consecutive points or vertices of a quadrilateral. 

Adjacent Sides: Adjacent or consecutive sides of a polygon is a polygon that have the common vertex.

Opposite Angles: Opposite angles are non-adjacent angles in a polygon.

Adjacent Angles: Adjacent angles are a pair of angles that have a common side and a common endpoint or vertex.

Perpendicular Diagonals: Perpendicular diagonals are diagonals whose intersections make 90°.

Mutually Bisecting Diagonals: The diagonals that cut each other exactly in half are called mutually bisecting diagonals.

Diagonals Bisecting Angles: The diagonals bisecting angles are the diagonals that bisects the four vertices in to equal angles.

Line of Symmetry: Line of symmetry is a line that divides the two-dimensional figure in to two equal parts that are reflection of each other.

Polygons

Regular Polygon: A regular polygon is a convex polygon with congruent sides and angles. 

Simple Polygon: A simple polygon is a closed figure which does not have common points or congruent sides.

Pentagon: Pentagon is a five sided polygon with the angle sum of 540°.

Hexagon: Hexagon is a six sided polygon with the angle sum of 720°

Heptagon: Heptagon is a seven sided polygon with the angle sum of 900°.

Octagon: Octagon is an eight sided polygon with the angle sum of 1080°.

Nonagon: Nonagon is a nine sided polygon with the angle sum of 1260°.

Decagon: Decagon is a ten sided polygon with the angle sum of 1440°.

Dodecagon: Dodecagon is a twelve sided polygon with the angle sum of 1800°.

N-gon: N-gon is a polygon with n number of sides.

Vertex: Vertex of a polygon is a point where rays, lines, or segments intersect.

Diagonal: Diagonal of a polygon is a line segment that connects one vertex with the other.

Convex Polygon: A polygon with interior angles less than 180° is called convex polygon.

Concave Polygon: Any polygon with angle measuring more than 180° are called concave polygon.

Perimeter: Perimeter of a polygon is the total length of all its sides.

Circles

Center, Diameter, and Radius: The midpoint of a circle is the center. The line segment that connects one end to another is called diameter. The distance between the center and any point of the circle is called radius.

Tangent Line: A tangent line is a line drawn perpendicular to the radius that touches only a single point on the circle.

Chord: A chord is a line segment inside a circle that connects two points on the circle.

Sector: A sector is one part of a circle that is surrounded by an arc and two radii.

Semicircle: A semicircle is a pair of arcs of a circle that are divided by diameter.

Arc, Major, and Minor: An arc is a curved line. The major arc is the intersection of a circle with the exterior and the central angle. The minor arc is the intersection of a circle with the interior and the central angle.

Folding and Reflecting

Reflection: Reflection is the mirror image of an object.

Image: An image is a two dimensional picture that has definite height and width.

Hamburger and Hotdog Fold: In hamburger, fold the paper in to half along the longer side. In Hotdog, fold the paper in to half along the shorter side.

Line of Symmetry: A line of symmetry is a line segment drawn through a geometric figure that makes two equal halves.

Other Terms

Congruent: Congruent figure have same shape and size.

Similar: Similar figure have same shape but not necessarily the same size.

Simple Closed Curve: Simple closed curves are the curves that do not meet and has no endpoints.

Sphere: A sphere is a perfect round figure that is equidistant from the point called the center of the sphere.

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