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