## Geometry

Geometry is a branch of mathematics that deals with shapes and their properties - points, lines, planes and solids. For other math terms see Algebra and Trigonometry.

### Math Symbols

- Algebra symbols / Angle and Line symbols / Basic Math symbols / Bracket symbols / Equivalence symbols / Geometry symbols / Greek alphabet / Roman numerals

### Nomenclature & Symbols for Engineering, Mathematics, & Science

- A - B - C - D - E - F - G - H - I - J - K - L - M - N - O - P - Q - R - S - T - U - V - W - X - Y - Z

## Geometry Terms

### A

- Acute angle - An angle that measures less than 90°.

- Adjacent angle - Two angles on a plane having the same vertex and a common line.

- Adjacent side - Next to the angle in a general triangle or next to the angle of the hypotenuse of a right triangle.

- Algorithm - A procedure used to solve a problem or a desired result.

- Altitude - The shortest distance from the base to the apex.

- Angle - Two rays sharing a common point.

- Angle bisector - A line that divides an angle into two equal angles.

- Antipodal point - Two points directly opposite each other on a sphere.

- Apex - The vertex at the tip of a cone or pyramid.

- Apothem - A line segment from the center of a regular polygon to the mid point of a side.

- Arc length - The distance along the arc or the circumference of a circle or any curve.

- Area - The inside space of a figure.

- Axiom - A statement accepted as true without proof.

### B

- Base - The bottom of a figure in either plane or solid geometry. If the bottom and top are parallel then either can be called base.

- Base area - The base surface area of a solid figure.

- Bisect - Divide into two congruent parts.

### C

- Center of a circle - A point at a fixed equal distance from all points of the circumference of a circle.

- Central angle - An angle in a circle with the vertex at the circle's center.

- Centroid - The center of a plane or mass.

- Cevian - A line that extends from a vertex of a triangle to the opposite side.

- Chord - A line segment on the interior of a circle.

- Circle - All points are at a fixed equal distance from a center point.

- Circumcenter - The point of intersection of the perpendicular bisectors of the sides.

- Circumscribed circle (circumcircle, outradius) - A circle that passes through all the vertices of a two-dimensional figure.

- Circumscribed (outside) - A sphere that touches every vertex.

- Circumscribed sphere - A polyhedron is a sphere that contains the polyhedron and touches each of the ployhedron's vertices.

- Circumference - The outside of a circle or a complete circular arc.

- Collinear - When three or more points lie on a straight line.

- Collinear points - Points that lie on the same line.

- Concave - An internal angle is greater than 180°.

- Concentric - Like geometric figures that share a common center.

- Concurrent - Lines or curves that all intersect at a single point.

- Conditional - An if... then... statement.

- Congruent - All sides having the same lengths and angles measure the same.

- Congruent lines - Line segments having the same length but not necessarily the same angle.

- Conic section - A section on any plane through a circle, ellipse, hyperbola, and parabola.

- Convex - No internal angle is greater than 180°.

- Coplanar - Lines and points lying on the same plane.

- Coplanar points - Points that lying on the same plane.

### D

- Diagonal - A line from one vertices to another that is non adjacent.

- Directrix - The path followed by a point or line when moving.

### E

- Edge - A line where two or more vertices come together.

- Ellipse - A two-dimensional figure with a conic section or a stretched circle.

- Ellipsoid - A three-dimensional figure sphere like surface for which all cross sections are ellipses.

- Euler line - The centroid, circumcenter, and orthocenter of any triangle always lies on a straight line.

- Euler's number - \(\large{ e=2.718281828749... }\)

- Expression - Any combination of numbers and variables used to create a mathematical expression or formula.

- Exterior angle - An angle on the exterior of two rays of a plane figure.

### F

- Face - Any flat surface of a solid figure.

- Foci - Two fixed points on the interior of an ellipse used to define the curve.

- Focus - The points that construct a conic section.

- Full angle - An angle that measures 360°.

### G

- Golden ratio (divine porportion, golden mean, golden section) - A mathematical ratio commonly found in nature and design. \(\large{ \varphi=1 : 1.6180339887... }\)

- Generatrix - A point or line when moved along a certain path creates a new shape.

- Geometric figure - Any set of points on a plane or in space.

### H

- Hexahedron - Any polyhedron with six faces.

- Horizontal - Parallel to a flat or level surface of the earth.

- Hyporenuse - The side of right triangle opposite the right angle, which is the longest side.

- Hypothesis - A tentative statement that might be true. Identify the problem, research the problem, then make a proposed solution to the problem.

### I

- Incenter - The point where the angle bisectors meet for a regular polygon or triangle.

- Incircle - A circle that touches all lines of a figure.

- Initial side of an angle - The inside of a ray of an x-axis of an angle.

- Inradius - The radius of a inscribed circle.

- Inscribed (inside) - A sphere that touches the center of every faces.

- Inscribed angle - An angle inside a circle with its vertex in the circle.

- Inscribed circle - The largest circle possible that can fit on the inside of a two-dimensional figure.

- Inscribed sphere (insphere) - A convex polyhedron is a sphere that is contained within the polyhedron and tangent to each of the polyhedron's faces.

- Inside angle - An angle on the interior of two rays of a plane figure.

- Interior angle - An angle on the interior of two rays of a plane figure.

- Intersecting lines - Lines that have only point in common.

- Interval - The region or space between two defined values.

### L

- Lateral surface area - The surface area of a solid figure excluding the area bases of the solid figure.

- Line - A straight path connecting two points.

- Line segment (segment) - All points bertween two points.

- Line segment bisector - A line or line segment that cuts another line segment into two equal parts.

- Locus - A set of points that form a geometric figure or graph.

- Long diagonal - Always crosses the center point of the figure.

### M

- Major arc - The longest of two arcs of a circle or ellipse.

- Major axis - The longest axis of a circle or ellipse.

- Mean - Another word for average.

- Median - The middle number in a data set.

- Median of a trapezoid - A line segment from the midpoint of the legs of a trapezoid.

- Median of a triangle - A line segment from a vertex (corner point) to the midpoint of the opposite side.

- Midpoint - A point on a line segment that divides the segment into two congruent segments.

- Midsphere - A polyhedron is a sphere that is tangent to every edge of the polyhedron.

- Minor arc - The shorter of two arcs of a circle or ellipse.

- Minor axis - Always the shortest axis of a circle or ellipse.

- Mixed number - A number written as a whole number and a fraction.

### N

- Non-collinear - Points that do not all lie on the same line.

- Non-collinear points - Points that do not all lie on the same line.

- Non-coplanar points - Points that do not all lie on the same plane.

- Non-polyhedron - Has a solid with curved edges or sides.

- Normal - In math it means to be at right angles.

### O

- Oblique - Tilted at an angle, not horizontal or vertical.

- Oblique cone - A three-dimensional figure with the apex not alligned above the center at 90° to the base.

- Oblique cylinder - A three-dimensional figure with both bases not alligned above each other and the center not at 90° to the other base center.

- Oblique prism - A three-dimensional figure with both bases not alligned above each other and the center not at 90° to the other base center.

- Oblique pyramid - A three-dimensional figure with the apex not alligned above the center at 90° to the base.

- Obtuse angle - An angle that measures more than 90°.

- Opposite angle (vertical angle) - The opposite angles when two lines intersect.

- Outlier - A data point in a data set that is far outside of an established pattern.

### P

- Parallel lines - Two lines that do not intersect.

- Parallel planes - Two planes that do not intersect.

- Perimeter - The sum of the lengths of all sides of a plane figure.

- Perpendicular - An angle that measures 90°.

- Perpendicular bisector - A line perpendicular to a segment passing through the segment's midpoint.

- Pi - \(\large{ \pi=3.1415926535 ... }\)

- Plane - An infinate expanse of points in two directions.

- Plane geometry - A two dimensional figure, also called planar geometry, with edges. The edges are line segments or edges and curve segments or arcs, all lying on a flat plane.

- Platonic solids - Each face is a regular polygon. There are five, cube, dodecahedron, icosahedron, octahedron, and tetrahedron.

- Point - A single location or the intersection of two lines.

- Polygon - A closed plane figure for which all edges are line segments and not necessarly congruent.

- Polyhedron - A three-dimensional figure that is a solid with no curved edges or sides.

- Porportional - Having a constant ratio.

- Prism solid - A prisim is a solids with two parallel ends that are exactly the same.

- Pyramid - A three-dimensional figure that is a polyhedron with a polygonal base and lateral faces that taper to an apex.

- Pyramid solid - A polyhedrons with a polygonal base and lateral faces that taper to an apex.

### Q

- Quadrilateral - A polygon with four sides.

- Quotient - The answer after dividing one number or expression by another.

### R

- Radical - A square root.

- Radius - A line segment between the center point and a point on a circle or sphere.

- Range - The difference between the largest and smallest nunbers in a data set.

- Ray - A line starting at a point and extending infinitely in one direction.

- Rectangular angle - Two rectangles with different lengths that intersect at a 90° angle at one end each.

- Reference angle - The smallest angle that the terminal side of a given angle makes with the x-axes.

- Reflection of a line section - Every point on a line segment appears an equal distance on the other side of a line.

- Right angle - An angle that measures 90°.

### S

- Sagitta - The perpendicular from the midpoint of the arc's chord to the arc itself.

- Scalene - If no two sides have the same length.

- Secant line - A line that passes through at least two points on a curve.

- Sector of a circle - A sector is a fraction of the area of a circle with a radius on each side and an arc.

- Segment (line segment) - All points bertween two points.

- Segment of a Circle - An interior part of a circle bound by a chord and an arc.

- Semi-major axis - Half of the longest axis of a circle or ellipse.

- Semi-minor axis - Half of the shortest axis of a circle or ellipse.

- Semicircle - Half of a circle.

- Semiperimeter - One half of the perimeter.

- Set - A defined group of objects.

- Side - Any line segment of an figure.

- Similar - Identical in shape, but not necessarily the same size.

- Skew lines - Lines that are not in the same plane and do not intersect.

- Skewed data - Not symmetric around the mean and the data (graph) has a long tail on one or the other.

- Short diagonal - Does not cross the center point of the figure.

- Solid geometry - A three-dimensional figure with connecting edges on multiple planes. The surface of each two-dimensional plane is called a face.

- Straight angle - An angle that measures 180° or pi radians.

- Standard position of an angle - An angle where its vertex is located at the origin and one ray is on the positive x-axis.

- Supplement of an angle - Any angle A between 0° and 180°. A is 180° - A

- Supplementary angles - Two angles that sum to 180°.

- Surface - A three-dimensional figure excluding internal points.

- Surface area - The total area of all the surfaces of a three dimensional figure.

- Symmetric - When two or more parts are congruent or identical to each other.

### T

- Terminal side of an angle - The inside of a ray of an angle oposite the x-axis initial side.

- Three-dimensional - A figure with height, width, and depth.

- Translation - Moving a shape to a new location with no other changes.

- Transversal - A line that intersects two other lines.

- Triangle exterior angle theorm - An exteroir angle is equal to the sum of the opposite interior angles.

- Triangle inequality theorem - Any side of a triangle is always shorter than the sum of the other two sides.

- Triangle inequality theorem converse - A triangle cannot be constructed from three line segments if any of them is longer than the sum of the other two.

- Two-dimensional - A flat figure.

### V

- Variable - A symbol used to represent a number that we do not know yet.

- Vector - A quantity with both magnitude and direction.

- Vertex - A point where two or more curves, edges, or lines meet.

- Vertices - Plural of vertex.

- Vertical - Perpendicular to horizontal or straight up or down.

- Vertical angle (opposite angle) - The opposite angles when two lines intersect.

- Volume - The amount of space in an solid figure.