Goemetry Gallery and Coordinate Geometry
... Proof: logical reasoning that uses facts, definitions, properties, and previously proven theorems to show that a proposition is true Syllogism (SIH-luh-jih-zuhm): a logical argument that always contains two premises and a conclusion; syllogisms have the following form: If a, then b. If b, then c. Th ...
... Proof: logical reasoning that uses facts, definitions, properties, and previously proven theorems to show that a proposition is true Syllogism (SIH-luh-jih-zuhm): a logical argument that always contains two premises and a conclusion; syllogisms have the following form: If a, then b. If b, then c. Th ...
Geometry Course Outline Learning Targets Unit 1: Proof, Parallel
... 31-1-1 Develop a formula for the sum of the measures of the interior angles of a polygon. 31-1-2 Determine the sum of the measures of the interior angles of a polygon. 31-2-1 Develop a formula for each interior angle measure of a regular polygon. 31-2-2 Determine the measure of each exterior angle o ...
... 31-1-1 Develop a formula for the sum of the measures of the interior angles of a polygon. 31-1-2 Determine the sum of the measures of the interior angles of a polygon. 31-2-1 Develop a formula for each interior angle measure of a regular polygon. 31-2-2 Determine the measure of each exterior angle o ...
3-D Figures
... Two Point Perspective – two types of parallel lines meet at vanishing points and one type is drawn parallel. To draw in two point perspective: 1. Draw horizon and 2 vanishing points. 2. Draw the front vertical edge of your figure. 3. Connect both ends of the edge to both vanishing points. Draw the ...
... Two Point Perspective – two types of parallel lines meet at vanishing points and one type is drawn parallel. To draw in two point perspective: 1. Draw horizon and 2 vanishing points. 2. Draw the front vertical edge of your figure. 3. Connect both ends of the edge to both vanishing points. Draw the ...
Curriculum Map Unit 4 Triangle Congruence
... angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints. G.CO.10: Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; t ...
... angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints. G.CO.10: Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; t ...
Geometry Review Packet 1
... 2) If two lines in a plane are cut by a transversal to form congruent corresponding angles, then the lines are parallel. 3) If two lines in a plane are cut by a transversal to form congruent alternate interior angles, then the lines are parallel. 4) If two lines in a plane are cut by a transversal t ...
... 2) If two lines in a plane are cut by a transversal to form congruent corresponding angles, then the lines are parallel. 3) If two lines in a plane are cut by a transversal to form congruent alternate interior angles, then the lines are parallel. 4) If two lines in a plane are cut by a transversal t ...
x – 1
... Median – A line from the midpoint to the vertex Where they all meet is the CENTROID The distance from the Centroid to the vertex is 2\3 the median. ...
... Median – A line from the midpoint to the vertex Where they all meet is the CENTROID The distance from the Centroid to the vertex is 2\3 the median. ...
Geometry
... c) two secant lines d) a tangent line and a chord. Investigate and apply theorems related to the measure of external angles drawn from a point outside a circle created by two tangent lines, two secant lines, or a tangent and a secant line. Investigate, justify, and apply theorems regarding chords of ...
... c) two secant lines d) a tangent line and a chord. Investigate and apply theorems related to the measure of external angles drawn from a point outside a circle created by two tangent lines, two secant lines, or a tangent and a secant line. Investigate, justify, and apply theorems regarding chords of ...
Cartesian coordinate system
A Cartesian coordinate system is a coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances from the point to two fixed perpendicular directed lines, measured in the same unit of length. Each reference line is called a coordinate axis or just axis of the system, and the point where they meet is its origin, usually at ordered pair (0, 0). The coordinates can also be defined as the positions of the perpendicular projections of the point onto the two axes, expressed as signed distances from the origin.One can use the same principle to specify the position of any point in three-dimensional space by three Cartesian coordinates, its signed distances to three mutually perpendicular planes (or, equivalently, by its perpendicular projection onto three mutually perpendicular lines). In general, n Cartesian coordinates (an element of real n-space) specify the point in an n-dimensional Euclidean space for any dimension n. These coordinates are equal, up to sign, to distances from the point to n mutually perpendicular hyperplanes.The invention of Cartesian coordinates in the 17th century by René Descartes (Latinized name: Cartesius) revolutionized mathematics by providing the first systematic link between Euclidean geometry and algebra. Using the Cartesian coordinate system, geometric shapes (such as curves) can be described by Cartesian equations: algebraic equations involving the coordinates of the points lying on the shape. For example, a circle of radius 2 in a plane may be described as the set of all points whose coordinates x and y satisfy the equation x2 + y2 = 4.Cartesian coordinates are the foundation of analytic geometry, and provide enlightening geometric interpretations for many other branches of mathematics, such as linear algebra, complex analysis, differential geometry, multivariate calculus, group theory and more. A familiar example is the concept of the graph of a function. Cartesian coordinates are also essential tools for most applied disciplines that deal with geometry, including astronomy, physics, engineering and many more. They are the most common coordinate system used in computer graphics, computer-aided geometric design and other geometry-related data processing.