SOLID MENSURATION

PLANE AND 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

\

PARTS OF SOLIDS

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

\

TYPES OF SOLIDS

• 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

\

SPECIAL TYPES OF SOLIDS

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

\

BASIC MATHEMATICAL CONCEPTS

\
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 AND POLYGONS

\
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

\
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

\
\
\
\
\
\
\
\
\
\
\
\
\
\
\
\
\
\
\
\
\
\
\
\
\
\
\
\