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Geometry 2

rename
Updated 2009-02-28 17:18
ShapeProperties
TriangleA 3-sided Polygon in which any 3 sides a,b,c satisfy a+b>=c.
TriangleA 3-sided Polygon where all internal angles A,B,C total to 180 degrees.
TriangleA 3-sided Polygon in which the 3 sides a,b,c and 3 internal angles A,B,C satisfy the Law of Sines:
a/sin(A)=b/sin(B)=c/sin(C).
TriangleA 3-sided Polygon in which any 3 sides a,b,c and the 3 internal angles A,B,C opposite them satisfy the Law of Cosines:
c2 = a2 - 2 a b cos(C) + b2.
Equilateral TriangleA Triangle with all sides a,b,c the same length and all internal angles A,B,C equal to 60 degrees.
Isosceles TriangleA Triangle with 2 sides a,b the same length and the 2 internal angles A,B opposite these sides the same measure.
Right TriangleA Triangle in which the largest internal angle is 90 degrees.
Right TriangleA Triangle in which
the 3 sides a,b,c satisfy the
Pythagorean Theorem: a2+b2=c2 where c is the
hypotenuse (the longest side).
Right Isosceles TriangleA Triangle with one 90 degree and two 45 degree internal angles.
Right TriangleA Triangle with sides in the ratio 3:4:5.
Right TriangleA Triangle with sides in the ratio 5:12:13.
Right TriangleA Triangle with sides in the ratio of a Pythagorean Triple.
memorize

 

See Pythagorean Theorem for a list of Pythagorean Triples.

 

ShapeProperties
RectangleA 4-sided Polygon with all internal angles equal to 90 degrees.
SquareA Rectangle with all sides the same length.
TrapezoidA 4-sided Polygon with 2 sides parallel and 2 sides not parallel.
RhombusA 4-sided Polygon shaped like a diamond on a deck of cards.
RhombusA 4-sided Polygon where all sides are the same length and opposite angles have the same measure.
KiteA 4-sided Polygon where 2 sets of adjacent sides have the same length and 1 set of opposite angles have the same measure. It has one axis of symmetry. It is like 2 isosceles triangles end to end.
ParallelogramA 4-sided Polygon with opposite sides the same length and opposite angles the same measure.
ParallelogramA 4-sided Polygon with opposite sides parallel to each other.
ParallelogramCould be a Rectangle, Square, or Rhombus.
QuadrilateralCould be a Trapezoid, Kite, or Parallelogram.
QuadrilateralA 4-sided Polygon where all internal angles total to 360 degrees.
Pentagon A 5-sided Polygon where all internal angles total to 540 degrees.
HexagonA 6-sided Polygon where all internal angles total to 720 degrees.
OctagonAn 8-sided Polygon where all internal angles total to 1080 degrees.
PolygonAn n-sided figure where all external angles total to 360 degrees and all internal angles total to 180 n - 360 degrees.
CircleAll points equidistant from a central point in 2-dimensions.
SphereAll points equidistant from a central point in 3-dimensions.
memorize

 

Fill in the blanks for the following:

 

StatementMissing Words
Two triangles are congruent if each has ___all 3 sides and all 3 internal angles the same.
Two triangles are congruent if each has ___all 3 sides the same (SSS).
Two triangles are congruent if each has ___1 side and any 2 internal angles the same (ASA or AAS).
Two triangles are congruent if each has ___1 internal angle and the 2 sides connected by this angle the same (SAS).
Two triangles are not necessarily congruent if each has ___1 internal angle and two sides (one adjacent to the angle and one opposite the angle) the same (SSA).
Two triangles are similar but not necessarily congruent if each has ___all 3 internal angles the same (AAA).
memorize

 

See Geometry, Math, or http://www.mathsisfun.com/geometry/plane-geometry.html for more.

 

See http://www.mathsisfun.com/numbers/pythagorean-triples.html for Pythagorean Triples.

 

See http://www.mathsisfun.com/algebra/trig-solving-triangles.html for congruent triangles.