Geometry Step by Step from the Land of the Incas is an interactive website, created by Antonio Gutierrez, that offers a variety of resources for teaching and learning about geometry, including music that plays in the background. The website mixes sound, science, and Incan history in order to raise students' interest in Euclidean geometry. On this website, visitors will find geometry problems, proofs, quizzes, puzzles, quotations, visual displays, photographs of Incan ruins, and "scientific speculation." The interactive aspects take some getting used to but also allow from some involved problem-solving activities.
composing
internetscout
mathematical
includes
given two congruent figures, describe a sequence that exhibits the congruence between them.
bisecting a segment
1. Derive the equation of a circle of given center and radius using the Pythagorean Theorem
euclidean
incan
NSDL
copying an angle
apply these techniques in the context of solving real-world and mathematical problems.
constructing perpendicular lines, including the perpendicular bisector of a line segment
use coordinates to find the length of a side joining points with the same first coordinate or the s
apply
Grade
lengths
edge
and constructing a line parallel to a given line through a point not on the line.
points on a perpendicular bisector of a line segment are exactly those equidistant from the segment
Mathematics
area
fractional
Internet Scout Project
packing
bisecting an angle
derive the formula for the area of a sector.
given two similar two-dimensional figures, describe a sequence that exhibits the similarity between
Mathematics -- History
eclectic
into
prism
the Pythagorean Theorem proved using triangle similarity.
1. Find the area of right triangles, other triangles, special quadrilaterals, and polygons by compos
the radius of a circle is perpendicular to the tangent where the radius intersects the circle.
when a transversal crosses parallel lines, alternate interior angles are congruent and correspondin
decomposing
intended
paradata
polygons
explain using similarity transformations the meaning of similarity for triangles as the equality of
1. Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, b
1. Prove that all circles are similar.
[S103F567]
Geometry
interest
other
given two figures, use the definition of congruence in terms of rigid motions to decide if they are
describe transformations as functions that take points in the plane as inputs and give other points
1. Give an informal argument for the formulas for the circumference of a circle, area of a circle, v
inscribed angles on a diameter are right angles
context
history
more
Incas
History/Policy/Law
complete the square to find the center and radius of a circle given by an equation.
give an informal derivation of the relationship between the circumference and area of a circle.
#composing
#internetscout
#mathematical
#includes
#giventwocongruentfigures,describeasequencethatexhibitsthecongruencebetweenthem.
#bisectingasegment
#1.DerivetheequationofacircleofgivencenterandradiususingthePythagoreanTheorem
#euclidean
#incan
#NSDL
#copyinganangle
#applythesetechniquesinthecontextofsolvingreal-worldandmathematicalproblems.
#constructingperpendicularlines,includingtheperpendicularbisectorofalinesegment
#usecoordinatestofindthelengthofasidejoiningpointswiththesamefirstcoordinateorthes
#apply
#Grade
#lengths
#edge
#andconstructingalineparalleltoagivenlinethroughapointnotontheline.
#pointsonaperpendicularbisectorofalinesegmentareexactlythoseequidistantfromthesegment
#Mathematics
#area
#fractional
#InternetScoutProject
#packing
#bisectinganangle
#derivetheformulafortheareaofasector.
#giventwosimilartwo-dimensionalfigures,describeasequencethatexhibitsthesimilaritybetween
#Mathematics--History
#eclectic
#into
#prism
#thePythagoreanTheoremprovedusingtrianglesimilarity.
#1.Findtheareaofrighttriangles,othertriangles,specialquadrilaterals,andpolygonsbycompos
#theradiusofacircleisperpendiculartothetangentwheretheradiusintersectsthecircle.
#whenatransversalcrossesparallellines,alternateinterioranglesarecongruentandcorrespondin
#decomposing
#intended
#paradata
#polygons
#explainusingsimilaritytransformationsthemeaningofsimilarityfortrianglesastheequalityof
#1.Knowprecisedefinitionsofangle,circle,perpendicularline,parallelline,andlinesegment,b
#1.Provethatallcirclesaresimilar.
#[S103F567]
#Geometry
#interest
#other
#giventwofigures,usethedefinitionofcongruenceintermsofrigidmotionstodecideiftheyare
#describetransformationsasfunctionsthattakepointsintheplaneasinputsandgiveotherpoints
#1.Giveaninformalargumentfortheformulasforthecircumferenceofacircle,areaofacircle,v
#inscribedanglesonadiameterarerightangles
#context
#history
#more
#Incas
#History/Policy/Law
#completethesquaretofindthecenterandradiusofacirclegivenbyanequation.
#giveaninformalderivationoftherelationshipbetweenthecircumferenceandareaofacircle.