Geometry Final

Front 1

Polyhedron is derived from...

Back 1

the greek words poly meaning many and edra meaning face.

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Polyhedron

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a three-dimensional geometric figure whose sides are polygons

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face

Back 3

a flat surface of a polyhedron

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edge

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the intersection of the faces in a polyhedron

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lateral face

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the face that joins the bases of a polyhedron

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vertex

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a point where two or more straight lines meet

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Apex

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The highest point in the polyhedron

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prism

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a solid figure whose bases are congruent and parallel to one another and whose sides are parallelograms

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bases

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the upper and lower parallel faces of the prism

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prisms are named...

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according to the shape of their base

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regular pyramid

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is a polyhedron with a base of a regular polygon and a vertex point that lies directly over the center of the base.

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Name the five regular polyhedra

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Tetrahedron
hexahedron
octahedron
dodecahedron
icosahedron

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tetrahedron

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a polygon with four faces

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hexahedron

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a polyhedron with six faces

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octahedron

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a polyhedron with eight faces

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dodecahedron

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a polyhedron with 12 faces

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icosahedron

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a polyhedron with 20 faces

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cylinder

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a three dimensional closed surface bounded on two ends by circular bases

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Cone

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a three dimensional curved surface having a circle as a base

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Sphere

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a round solid figure with every point on its surface equidistant from its surface

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Surface area

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the total area of the surface of a three dimensional object

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Lateral area

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The sum of all the sides of a 3-D object excluding its bases

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Lateral faces

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the faces of a prism that aren't bases

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Lateral edges

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segments that are formed when faces meet

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Altitude

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the segment that is perpendicular to and connects to the base

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Arc

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is a curved segment that is part of the circumference of a circle

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a central angle of a circle

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is an angle with its vertex at the center of a circle

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the measure of a minor arc

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is the measure of its central angle

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the measure of a semicircle

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is 180 degrees

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the measure of a major arc will always

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be greater that 180 degrees

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chord

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a line segment that joins two points on the circumference of a circle

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a diameter that is perpendicular to a chord...

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bisects the chord and the arc

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inscribed angle

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is an angle formed by two chords that meet at the same point on a circle

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the measure of an inscribed angle is equal to

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1/2 the measure of the intercepted arc

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if two inscribed angles intercept the same arc...

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then the angles are congruent

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an angle inscribed in a semicircle...

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is a right angle

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if a quadrilateral is inscribed in a circle then...

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its opposite angles are supplementary

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the measure of an angle formed by two chords that intersect inside a circle...

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is equal to 1/2 the sum of the measure of the intercepted arcs

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a tangent to a circle

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is a line or segment in the plane of the circle that touches the circle at exactly 1 pt.

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the point that the tangent line makes with the circle is referred to as

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the point of tangency

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Secant

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a line that contains a chord

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the measure of an angle formed by a chord and a tangent is equal to

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1/2 the measure of the intercepted arc

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the measure of an angle formed by two secants ttwo tangiest or a secant and a tangent drawn from a point outside a circle is equal to

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1/2 the difference of the measure of the intercepted arcs

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sector of a circle

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is a region bounded by two radii and an arc of the circle

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segment

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is a region bounded by a chord and the minor arc that it cuts

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if a tangent and a secant intersect outside a circle, then the square of the measure of the tangent equals

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the product of the measures of the secant and its external portion

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if two tangent segments intersect outside a circle,

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then the tangents segments must have equal measures

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two triangles are congruent if

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their corresponding sides are equal in length and their corresponding angles are equal in size

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what are the four euclidean transformations?

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Rotations
Translations
Reflections
Glide Reflections

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Another word for tessellation is..

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Tiling

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a regular tessellation is made up of the

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same congruent regular polygons

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the arrangement of regular polygons at every vertex

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must be identical

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What three regular polygons can tessellate in the euclidean plane

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Triangles
squares
hexagons

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semi-regular tessellation

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1. it is formed by two or more polygons
2. the arrangement at every vertex pt. is identical