SOLID MENSURATION
SOLID MENSURATION - also known as solid geometry, it is the study of various solids (Volume Area, Height, etc.)
SOLID - any limited portion of space bounded by surfaces of plane figures
PLANE FIGURE - two dimensional
SOLID FIGURE - three dimensional
EDGES - the intersection of the bounding plane
FACES - the portions of the bounding planes included by the edges
VERTICES - the intersections of the edge
DIAGONALS - are any straight lines joining any two vertices that are not in the same face
SECTION - plane figure formed by the intersection of a plane and a solid
RIGHT SECTION - a section of solid that is perpendicular to one of its lateral edges
CUBE
RECTANGULAR PRISM
TRIANGULAR PRISM
CYLINDER
SPHERE
CONE
PYRAMID
VOLUME OF A SOLID - a volume of a solid is the amount of space it occupies. It is denoted in units of cubic length
AREA OF A PLANE - the space enclosed by the boundary of a plane figure. It is denoted in units of square length
SURFACE AREA OF A SOLID - also known as Total Surface area, it is the area of a 3-dimensional surface or solid
LATERAL AREA OF A SOLID - areas of the lateral or side surfaces except for the base and top
POLYHEDRON - is a solid which is bounded by polygons joined at their edges
- REGULAR - made of the same, regular polygons
- IRREGULAR - made of the same or different irregular polygons
PLATONIC SOLIDS OR REGULAR POLYHEDRA - solids that have polygonal faces that are similar in form, height, angles, and edges. It is also a 3-dimensional convex and regular solid
- TETRAHEDRON
- CUBE
- OCTAHEDRON
- DODECAHEDRON
- ICOSAHEDRON
IRREGULAR POLYHEDRA -
- PRISM - a solid shape that is bound on all its sides by plane faces
- PYRAMID - is a polyhedron formed by connecting a polygonal base and a point, called the apex. Each base edge and apex form a triangle, called a lateral face
SIMILAR SOLIDS - two or more solids that have the same shape but not the same size
AXIOM METHOD - used to arrive at a theory based on axioms
AXIOMS/POSTULATES - self-evident statements that do not require proof
THEOREMS - statements that need to be proved
PROPOSITION - same definition, but of lesser importance than a theorem
LEMMA - a proven statement used to prove a theorem
COROLLARY - statements consequent to the theorem
POINT - a fixed location in space represented by a dot
LINES - is contained within two points and extends indefinitely in two opposite directions
LINE SEGMENT - line with two endpoints
RAY - a portion of a line that consists of an endpoint and a set of all points on one side of the line
COLLINEAR POINTS - points that lie on the same line
NONCOLLINEAR POINTS - no line on which all of the points lie
PLANE - a flat surface that extends indefinitely. Three noncollinear points determine a plane
COPLANAR POINTS - are points that lie on the same plane
PARALLEL LINES - are lines in the same plane that have no points in common
SKEW LINES - non-coplanar lines that do not parallel nor intersect
PARALLEL PLANES - planes that do not intersect
ANGLES - set of all points that are the union of rays having the same endpoint. It may be named using capital letters, Greek letters, or three capital letters
TYPES OF ANGLES
NAME | SIZE OF ANGLE |
---|---|
ACUTE ANGLE | 0-90 degrees |
RIGHT ANGLE | exactly 90 degrees |
OBTUSE ANGLE | 90-180 degrees |
STRAIGHT ANGLE | exactly 180 degrees |
REFLEX ANGLE | 180-360 degrees |
360 ANGLE | one complete rotation or revolution |
VERTICAL ANGLES - angles lying on opposite sides or a pair of non-adjacent angles formed by two lines that are intersecting
CONGRUENT ANGLES - have the same angle measure
ALTERNATE EXTERIOR ANGLES - pair of angles that are formed on the other side of the parallel lines but on the opposite side of the transversal
CORRESPONDING ANGLES - angles formed in matching corners or corresponding corners with the transversal
DIHEDRAL ANGLE - an angle formed by two intersecting planes
ADJACENT DIHEDRAL ANGLE - two dihedral angles having a common edge and a common face
PERPENDICULAR PLANES - are two intersecting planes that form a right dihedral angle
POLYHEDRAL ANGLE - an angle formed by three or more intersecting planes at a common point or vertex
TYPES OF POLYHEDRAL ANGLES
tetrahedral
pentahedral
hexahedral
heptahedral
POLYGON - closed plane figure formed by three or more line segments
SIDES - line segments
VERTEX - the intersection of two sides in a polygon
CONSECUTIVE SIDES - are sides that share a common vertex
CONSECUTIVE VERTICES - two endpoints of any side of a polygon
DIAGONAL - a line segment whose endpoints are nonconsecutive vertices of a polygon
CONVEX POLYGON - where diagonals lie inside of a polygon
CONCAVE POLYGON - where diagonals lie outside of a polygon
EQUILATERAL - congruent sides
EQUIANGULAR - congruent angles
REGULAR POLYGON - a polygon that is both equilateral and equiangular
SOLID MENSURATION - also known as solid geometry, it is the study of various solids (Volume Area, Height, etc.)
SOLID - any limited portion of space bounded by surfaces of plane figures
PLANE FIGURE - two dimensional
SOLID FIGURE - three dimensional
EDGES - the intersection of the bounding plane
FACES - the portions of the bounding planes included by the edges
VERTICES - the intersections of the edge
DIAGONALS - are any straight lines joining any two vertices that are not in the same face
SECTION - plane figure formed by the intersection of a plane and a solid
RIGHT SECTION - a section of solid that is perpendicular to one of its lateral edges
CUBE
RECTANGULAR PRISM
TRIANGULAR PRISM
CYLINDER
SPHERE
CONE
PYRAMID
VOLUME OF A SOLID - a volume of a solid is the amount of space it occupies. It is denoted in units of cubic length
AREA OF A PLANE - the space enclosed by the boundary of a plane figure. It is denoted in units of square length
SURFACE AREA OF A SOLID - also known as Total Surface area, it is the area of a 3-dimensional surface or solid
LATERAL AREA OF A SOLID - areas of the lateral or side surfaces except for the base and top
POLYHEDRON - is a solid which is bounded by polygons joined at their edges
- REGULAR - made of the same, regular polygons
- IRREGULAR - made of the same or different irregular polygons
PLATONIC SOLIDS OR REGULAR POLYHEDRA - solids that have polygonal faces that are similar in form, height, angles, and edges. It is also a 3-dimensional convex and regular solid
- TETRAHEDRON
- CUBE
- OCTAHEDRON
- DODECAHEDRON
- ICOSAHEDRON
IRREGULAR POLYHEDRA -
- PRISM - a solid shape that is bound on all its sides by plane faces
- PYRAMID - is a polyhedron formed by connecting a polygonal base and a point, called the apex. Each base edge and apex form a triangle, called a lateral face
SIMILAR SOLIDS - two or more solids that have the same shape but not the same size
AXIOM METHOD - used to arrive at a theory based on axioms
AXIOMS/POSTULATES - self-evident statements that do not require proof
THEOREMS - statements that need to be proved
PROPOSITION - same definition, but of lesser importance than a theorem
LEMMA - a proven statement used to prove a theorem
COROLLARY - statements consequent to the theorem
POINT - a fixed location in space represented by a dot
LINES - is contained within two points and extends indefinitely in two opposite directions
LINE SEGMENT - line with two endpoints
RAY - a portion of a line that consists of an endpoint and a set of all points on one side of the line
COLLINEAR POINTS - points that lie on the same line
NONCOLLINEAR POINTS - no line on which all of the points lie
PLANE - a flat surface that extends indefinitely. Three noncollinear points determine a plane
COPLANAR POINTS - are points that lie on the same plane
PARALLEL LINES - are lines in the same plane that have no points in common
SKEW LINES - non-coplanar lines that do not parallel nor intersect
PARALLEL PLANES - planes that do not intersect
ANGLES - set of all points that are the union of rays having the same endpoint. It may be named using capital letters, Greek letters, or three capital letters
TYPES OF ANGLES
NAME | SIZE OF ANGLE |
---|---|
ACUTE ANGLE | 0-90 degrees |
RIGHT ANGLE | exactly 90 degrees |
OBTUSE ANGLE | 90-180 degrees |
STRAIGHT ANGLE | exactly 180 degrees |
REFLEX ANGLE | 180-360 degrees |
360 ANGLE | one complete rotation or revolution |
VERTICAL ANGLES - angles lying on opposite sides or a pair of non-adjacent angles formed by two lines that are intersecting
CONGRUENT ANGLES - have the same angle measure
ALTERNATE EXTERIOR ANGLES - pair of angles that are formed on the other side of the parallel lines but on the opposite side of the transversal
CORRESPONDING ANGLES - angles formed in matching corners or corresponding corners with the transversal
DIHEDRAL ANGLE - an angle formed by two intersecting planes
ADJACENT DIHEDRAL ANGLE - two dihedral angles having a common edge and a common face
PERPENDICULAR PLANES - are two intersecting planes that form a right dihedral angle
POLYHEDRAL ANGLE - an angle formed by three or more intersecting planes at a common point or vertex
TYPES OF POLYHEDRAL ANGLES
tetrahedral
pentahedral
hexahedral
heptahedral
POLYGON - closed plane figure formed by three or more line segments
SIDES - line segments
VERTEX - the intersection of two sides in a polygon
CONSECUTIVE SIDES - are sides that share a common vertex
CONSECUTIVE VERTICES - two endpoints of any side of a polygon
DIAGONAL - a line segment whose endpoints are nonconsecutive vertices of a polygon
CONVEX POLYGON - where diagonals lie inside of a polygon
CONCAVE POLYGON - where diagonals lie outside of a polygon
EQUILATERAL - congruent sides
EQUIANGULAR - congruent angles
REGULAR POLYGON - a polygon that is both equilateral and equiangular