Plane & Solid Geometry

Polygon

A closed plane figure bounded by straight lines.

• geos - earth

• metron - measurement

The word geometry is taken from the Greek words ____ means ____ and ____ which means _____.

Geometry

A branch of mathematics which deals with questions of size, shape, and relative position of figures and with properties of space.

• Interior angles

• Number of sides

Polygons are named in accordance with the _____ and ______.

Regular Polygons

Polygons of equal length of the sides are called ______.

1. Convex Polygons

2. Concave Polygons

Classifications of Polygons based on their interior angles: (2)

Convex Polygons

Polygons with no interior angle greater than 180°.

Re-entrant Polygon

Concave polygon is also called?

Concave Polygon

Polygons with at least one angle greater than 180°.

Concave Polygons

A polygon in which you can draw at least one straight line that crosses more than two sides.

Regular Polygon

A polygon that is also equilateral and equiangular.

Euclid

Father of Geometry

Euclidean Geometry

Other term for Geometry?

Apothem

A line segment from the center of a regular polygon to the midpoint of a side.

Apothem

The radius of the incircle of the polygon.

Rectangle

A quadrilateral whose adjacent sides are perpendicular.

Quadrilateral

A polygon with four edges and four vertices.

Parallelogram

A quadrilateral whose opposite sides are parallel.

Square

A rectangle of equal sides.

Rhombus

A parallelogram of equal sides.

Trapezoid

A quadrilateral whose one pair of sides parallel to each other.

General Quadrilateral

A trapezium or ______ is a polygon with four sides.

Cyclic Quadrilateral

A quadrilateral inscribed in a circle.

Polyhedron

A closed space bounded by planes.

Rectangular Parallelepiped

A polyheron with six faces which are all rectangles.

Cube

A polyhedron with six faces which are all squares.

Prism

A polyhedron having two bases which are equal polygons in parallel planes and whose other faces are parallelograms.

1. Right Prism

2. Oblique Prism

Two types of Prism:

Right Prism

The lateral faces are perpendicular to the base.

Oblique Prism

The lateral faces are not perpendicular to the baseand appears to be slanted.

Prismatoid

A polyhedron having for bases two polygons in parallel planes, and for lateral faces triangles or trapezoids with one side lying in one bas, and the opposite vertex or side lying in the other base of the polyhedron.

Regular Polyhedron

A polyhedron whose faces are equal regular polygons, and all of whose polyhedral angles are equal.

Faces

The portions of the bounding planes included by the edges.

Vertices

The intersection of the edges.

1. Pythagoras

2. Hippasus

(1) ______ knew the existence of all the regular polyhedrons except the dodecahedron which was discovered in 470 B.C. by (2) ______.

Platonic Solids

The five regular polyhedrons are also known as the ______, although they were known to the Greeks before the time of Plato.

Leonhard Euler

Swiss Mathematician _______ showed that for any simple polyhedron, the sum of the number of vertices V and the number of faces F is equal to the number of edges plus 2.

Cylinder

A solid bounded by a closed cylindrical surface and two parallel planes which are the bases.

Right Circular Cylinder

A solid bounded by a closed cylindrical surface which are perpendicular to the circular bases.

Pyramid

A polyhedron whose base is a polygon of any number of sides with one face, called the base, and whose other face are triangles with a common vertex.

Frustum of a Pyramid

The portion between the base of a pyramid and a section parallel to the base.

Cone

A solid bounded by a conical surface (lateral surface) whose directrix is a closed curve, and a plane (base) which cuts all the elements.

Sphere

A solid bounded by a closed surface every point of which is equidistant from a fixed point called the center.

Spherical Lune

The portion of a spherical surface bounded by the halves of two great circles.

Spherical Zone

The portion of a spherical surface between two parallel planes. A ______ of one base has one boundinh plane tangent to the sphere.

Spherical Segment

The portion of a sphere bounded by a zone and the planes of the zone’s bases.

Spherical Wedge

The portion of the surface of a sphere included between two great semicircles having a common diameter.

Spherical Cone

A solid formed by the revolution of a circular sector about its one side (radius of the circle).

Spherical Pyramid

The portion of a sphere bounded by a spherical polygon and the planes of its sides.

Torus (Doughnut)

A solid formed by rotating a circle about an axis not passing the circle.

1. Oblate Spheroid

2. Prolate Spheroid

2 Types of Ellipsoid:

Oblate Spheroid

It is a special ellipsoid with c = a. A solid formed by rotating an ellipse about its minor axis.

Prolate Spheroid

It is a special ellipsoid with c = b. A solid formed by rotating an ellipse about the major axis.

Paraboloid

A solid formed by rotating a parabolic segment about its axis of symmetry.