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Transcript

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