Altitude

Altitude [al-ti-tyood]
Noun
The altitude (also known as the height) is line at right angle to a side that goes through the oposite vertex.

* Blue line is the altitude while the red lines are the triangle's edges. 

Vanishing Point

Vanishing Point [van-ish-ing point]
Noun
A vanishing point is a a certain location in a perspective drawing which receding parallel line, depending on how viewed, can alternate perspective. Allows a shape or figure to appear faintly closer or further (smaller/bigger) depending on how close and how it is placed in coloration with the vanishing point.      

Perspective Drawing

Perspective Drawing [per-spek-tiv draw-ing]
Noun
Perspective drawing is an accurate portrayal on a flat surface (usually facilitated by an isometric dot paper) of an image seen by the eyes. This type of drawing primarily focuses on perspective points and vanishing points on the paper,  allowing images to appear closer or further based on the designated drawing.

This is extremely important in geometry, for it allows one to create a clear representations of a 3D solid figure (usually very hard achieve).     

Isometric Dot Paper

Isometric Dot Paper [ahy-suh-me-trik dot pey-per]
Noun
An isometric dot paper (also known as 3D paper) is a type of graph paper which allows for more accurate drawing of solid figures. By having small dots all over the paper, it allows for the user to connect the dots, crating both edges and vertices with more facility.  

Diagonal

Diagonal [dahy-ag-uh-nl]
Noun
A diagonal is a straight line inside a shape that goes from one vertex to another (cannot intersect an edge). When we join two vertices of a polygon which isn't already joined by an edge, we get a diagonal.

*Both dotted lines are indeed diagonals 

Parallel Planes

Parallel Planes [par-uh-lel pleyn]
Noun
Parallel planes are planes that do not intersect and are indeed parallel. Two planes that aren't parallel (intersecting planes) intersect at a line.

An example of parallel planes are the walls and floor of a room; never intersecting.  

Platonic Solid

Platonic Solid [pluh-ton-ik sol-id]
Noun
A platonic solid is a 3D shape which has the following characteristics:

• each face is the same exact polygon 
• the same number of polygon meet at each vertex/corner   

Tetrahedron 3 triangles meet at each vertex 4 Faces 4 Vertices 6 Edges

Cube 3 squares meet at each vertex 6 Faces 8 Vertices 12 Edges

Dihedral Angle

Dihedral Angle [dahy-hee-druhl ang-guhl]
Noun
A dihedral angle is an angle formed in the intersection of two different planes. Not only is a dihedral angle important in geometry, but also in science since it is used to describe atom/molecule formation and in computer science.  

Volume

Volume [vol-yoom]
Noun
Volume is the amount of space/capacity a solid (3D) figure occupies. A way to think about volume is if you were to pour water in a box, the amount of water needed to fill that box is its volume. See the equations below to find the volume of each solid figure.

cube = a ³ 

rectangular prism = a b c 

irregular prism = b h 

cylinder = b h = pi r ² h 

pyramid = (1/3) b h 

cone = (1/3) b h = 1/3 pi r ² h 

sphere = (4/3) pi r ³ ellipsoid = (4/3) pi r₁ r₂ r₃  

Surface Area

Surface Area [sur-fis air-ee-uh]
Noun
Surface area in general, is the sum of the area of all shapes that covers the surface of a designated solid figure. Use the table below to find each solid figure's surface area equation.

Base Area

Base Area [beys air-ee-uh]
Noun
Base area is the area of a 3D figure's base.  As you will see in the table below, base area is very important to find both surface area and volume in an array of different solid figures. 

Figure	Volume	Lateral Surface Area	Area of theBase(s)	Total Surface Area
Box (also called rectangular parallelepiped, right rectangular prism)	lwh	2lh + 2wh	2lw	2lw + 2lh + 2wh
Prism	Bh	Ph	2B	Ph + 2B
Pyramid		-	B	-
Right Pyramid			B
Cylinder	Bh	-	2B	-
Right Cylinder	Bh	Ph	2B	Ph + 2B
Right Circular Cylinder	πR2h	2πRh	2πR2	2πRh + 2πR2
Cone		-	B	-
Right Circular Cone		πRs or	πR2	πRs + πR2 or

*Base area is 'B' in the above equations.

Oblique Prism

Oblique Prism [oh-bleek priz-uhm]
Noun
A prism where the bases are not alined with each other, unlike the right prism.

 As you can see in the solid above; all the lateral faces of an oblique prism are parallelograms.
    

Right Prism

Right Prism [rahyt priz-uhm]
Noun
A right prism is a prism which has its bases aligned one on top of the other while all of its lateral faces are rectangles.

   

*The above equations are applicable to Right Prisms

Cross Section

Cross Section [kraws sek-shuhn]
Noun
A cross section is the shape made by slicing straight through a solid figure.

Cross section is useful in geometry because it gives the shape when a 3D figure is cut through by a plane.   

Prism

Prism [priz-uhm]
Noun
A prism is a 3D object with the following characteristics:

• identical ends/bases
• flat sides
• same cross section along its length
• polyhedrons (all faces are flat and bases are polygons) 

* All the above solid objects are prisms

Polyhedron

Polyhedron [pol-ee-hee-druhn]
Noun
A polyhedron is a 3D solid figure which is composed of a collection of polygons as their faces.

Cube	Triangular Prism	Dodecahedron
Its faces are all squares	Its faces are triangles and rectangles	Its faces are pentagons

*All of the above figure are polyhedrons 

Lateral Face

Lateral Face [lat-er-uhl feys]
Noun

Lateral face is the face which are not the base, the face which compliment the base. They are formed by lateral edges.  

he figure above has a hexagon as base, hence the name hexagonal prism. There are 6 lateral edges which help form and connect the 6 lateral faces. 

Lateral Edge

Lateral Edge [lat-er-uhl ej]

Noun 

A lateral edge are the edges and points which form the lateral faces of a 3D figure.   

The figure above has a pentagon as base, hence the name pentagonal prism. There are 5 lateral edges which help form and connect the 5 lateral faces. 

Base

Base [beys]
Noun
A base is one side (in solid geometry a base can also be one or two faces)  of a polygon most commonly used as a reference for other measurements such as: area, surface area, perimeter, volume etc.

 

Triangles                            Quadrilaterals with a Pair of  Parallel Sides              Faces of a Solid 

A base are usually used in triangles, quadrilaterals with a pair of  parallel sides and faces of a solid figure. Definitely a key component to geometry allowing as to find wanted measurements of both two dimensional and three dimensional figures.  

Face

Face [feys]
Noun
In any 3D shape that is composed of flat surfaces, each of these surfaces are called a face. The line where two faces meet are considered an edge.  

For example, the triangular prism above has 5 faces, 2 of them being a triangle and the other 3 being rectangles. Also in this prism there are 9 edges.    

Edge

Edge [ej]
Noun
In a 3D shape that is composed and produced of faces, an edge is a line segment where two surfaces meet. Where 3 or more edges meet, a vertex is created.  

  

The rectangular prism above there are 6 faces, therefore since an edge is where two surfaces meet, there are 12 edges in the solid figure.  

Vertex

   

Vertex [vur-teks]
Noun
Plural: vertices [vur-tuh-seez]

A vertex is a common endpoint of two or more rays/line segments. 

Usually a vertex is a point/location where 2 lines meet.They are extremely important, a necessity in geometry especially when talking about shapes and figures. They can be used in 2D (a square has four vertices) and even with solid geometry, where since it is in a 3D plane, vertices are the point where 3 or more edges meet. Also in solid geometry, a vertex can also be called a corner.