Transcript Geometry Review - lowesgeometryprojects

Geometry Review
By: Kyle Dykes
Chapter 1
• Important Terms
– Line: extends in one dimension– Collinear Points: Points that lie on the same line
– Coplanar Points: Points that lie on the same plane
– Conjecture: An unproven statement that is based
on observation.
– Postulate: Rules that are accepted without proof
Chapter 1
• Postulates, Theorems and Formulas
– The Distance formula
– Pythagorean Theorem
– Midpoint Formula
Chapter 3
• Important Terms
– Parallel lines- if two lines are coplanar and do not
intersect
– Skew lines- lines that do not intersect and are not
coplanar
– Parallel Planes- planes that do not insersect
Chapter 3
• Postulates, Theorems and Formulas
– Consecutive interior angles- If two parallel lines
are cut by a transversal, then the pairs of alternate
interior angles are congruent.
– Alternate Exterior Angles- If two parallel lines are
cut by a transversal, then the pairs of alternate
exterior angles are congruent.
Chapter 4
• Important terms
– Triangle- a figure formed by three segments
joining three noncollinear points
• Theorems
– Triangle Sum Theorem
Chapter 6
• Important Terms
– Polygon- a plane figure that meets the following
conditions
– Convex- if no line in the polygon contains a point
in the interior of the polygon
• Postulates, Theorems and Formulas
– Interior Angles of a Quadrilateral. The sum of the
measures of the interior angles of a quadrilateral
is 360˚
Chapter 7
• Important Terms
– Image- a figure that has been reflected, rotated,
or translated
– Preimage- the original figure
• Postulates, Theorems and Formulas
– Theorem 7.2- a rotation is an isometry
Chapter 8
• Important Terms
– Scale factor- the ratio of the lengths of two
corresponding sides in two similar polygons
• Postulates, Theorems and Formulas
– Angle-Angle Similarity Postulate. If two angles of
one triangle are congruent to two angles of
another triangle, then the two triangles are similar
Chapter 9
• Important Terms
– Trigonometric ratio- a ratio of the lengths of two
sides of a right triangle. Sine, Cosine, and Tangent
• Postulates, Theorems and Formulas
– Theorem 9.1- if the altitude is drawn to the
hypotenuse of a right triangle, then the two
triangles formed are similar to the original triangle
and to each other
Chapter 10
• Important Terms
– Circle- the set of all points in a plane that are
equidistant from a given point, called the center
• Postulates, Theorems and Formulas
– Theorem 10.1- If a line is tangent to a circle, then
it is perpendicular to the radius drawn to the point
of tangency
Chapter 11
• Important Terms
– Apothem of a polygon- the distance from the
center to any side of the polygon
• Postulates, Theorems and Formulas
– Areas of Similar Polygons- if two polygons are
similar with the lengths of corresponding sides in
the ratio of a:b, then the ratio of their areas is a
squared : b squared
Chapter 12
• Important Terms
– Polyhedron- a solid that is bounded by polygons,
called faces, that enclose a single region of space
– Vertex- the point where three or more edges meet
• Postulates, Theorems and Formulas
– Euler’s Theorem- The number of faces (F), Vertices
(V), and edges (E) of a polyhedron are related by
the formula F+V= E+2