Solid Mensuration Definition of terms

Plane

a surface that a straight line joining two points in it lies wholly in the surface.

Plane Geometry

about flat shapes like lines, circles, triangles, etc. shapes that can be drawn on a

piece of paper.

plane figures

Figures which lie on a plane are called

Solid Geometry

is about three-dimensional objects like cubes, prisms, cylinders, spheres, etc.

solid figures

Figures which occupy a three dimensional space are called

two-dimensional shape

can be defined as a plane figure that can be drawn on a flat surface.

It has only two dimensions (length and width), with no thickness or depth.

three-dimensional shape

is any solid object that has three dimensions (length, width and

thickness).

Area

the number of space occupied by a two-dimensional figure.

Perpendicular

one straight line cuts another so as to make any two adjacent angles equal, each

line is perpendicular to the other.

Tangent

a straight line which, however far it may be produced, has only one

point in common with the circle.

Perimeter

of a shape is defined as the total distance around the shape.

Square

four sides are equal

Rectangle

two parallel sides are equal and four angles are 90°

Triangle

portion of a plane bounded by three straight lines.

Right Triangle

one angle measures 90°

Altitude of a Triangle

is a perpendicular from any vertex to the

side opposite, produced if necessary.

Hypotenuse

is the side opposite the right angle.

Parallelogram

opposite sides are parallel

Trapezoid

one pair of opposite sides are parallel

Circumference

distance around the circle

Radius

line segment that joins center to the boundary of a circle or sphere

Diameter

any straight line segment that passes through the center of the circle and whose

endpoints lie on the circle

Similar polygons

polygons that have their homologous angles equal and their homologous sides

proportional.

Similar polygons

have the same ratio as the squares of any two corresponding lines

Solid

any limited portion of space, bounded by surfaces

Section of a solid

plane figure cut from the solid by passing a plane through it.

Polyhedron

solid bounded by planes

edges of a polyhedron

are the intersections of the bounding planes

faces

are the portions of the bounding planes included y the edges.

vertices

intersections of the edges

cube

polyhedron whose six faces are all squares

equal

The three dimensions of a cube are ___to each other.

congruent

All the faces of a cube are ___ squares

rectangular parallelepiped

polyhedron whose all faces are rectangle.

equal

The parallel edges of a rectangular parallelepiped are ___.

opposite lateral faces

The_____ of a rectangular parallelepiped are equal and parallel.

base

Any two opposite faces of a rectangular parallelepiped may be taken as the ___.

Prism

a polyhedron of which two faces are equal polygons in parallel planes, and the other faces are

parallelograms.

bases

AB, the equal polygons;

lateral edges

e, intersections of lateral faces, are equal and

parallel.

lateral area

the sum of the areas of the remaining faces. (prism)

altitude

h, the perpendicular distance between the planes of its bases.

right section

K=Area of ___section perpendicular to the lateral edges.

right prism

prism whose lateral edges are perpendicular to its bases; its lateral faces are

rectangles.

equal

sections of a prism made by parallel planes cutting all the lateral edges are ___ polygons.

lateral area

___of a prism is equal to the product of lateral edge and the perimeter of the right section.

volume

___of a prism is equal either to the product of area of the base and the altitude, or to the product of

a right section and a lateral edge.

cylindrical surface

a surface generated by a moving straight line (generator) which is always parallel to

a fixed line, and which always intersects a fixed plane curve (directrix) not in the plane with the fixed line.

cylinder

solid bounded by a closed cylindrical surface and two parallel planes.

lateral surface

The bounding cylindrical surface of a cylinder

equal

The bases of a cylinder are __.

altitude

The __ of a cylinder is the perpendicular distance between the bases.

right section

of a cylinder is a section perpendicular to all elements of the cylinder.

lateral area

of a cylinder is equal to the product of an element and the perimeter of the right section.

volume

of a cylinder is equal either to the product of a base and the altitude, or to the product of a right

section and an element.