Quadrilaterals

... e) If a quadrilateral is a parallelogram, then the diagonals bisect each other. Each of these statements is called a conditional statement. The “if” part of the statement is called the hypothesis and the “then” part is called the conclusion. When the hypothesis and conclusion are reversed, the conve ...

... e) If a quadrilateral is a parallelogram, then the diagonals bisect each other. Each of these statements is called a conditional statement. The “if” part of the statement is called the hypothesis and the “then” part is called the conclusion. When the hypothesis and conclusion are reversed, the conve ...

Chapter 4: Congruent Triangles

... Example 1 Classify Triangles by Angles ARCHITECTURE The roof of this house is made up of three different triangles. Use a protractor to classify DFH, DFG, and HFG as acute, equiangular, obtuse, or right. DFH has all angles with measures less than 90, so it is an acute triangle. DFG and HFG bot ...

... Example 1 Classify Triangles by Angles ARCHITECTURE The roof of this house is made up of three different triangles. Use a protractor to classify DFH, DFG, and HFG as acute, equiangular, obtuse, or right. DFH has all angles with measures less than 90, so it is an acute triangle. DFG and HFG bot ...

Chapter 4: Congruent Triangles

... COORDINATE GEOMETRY Find the measures of the sides of ABC and classify each triangle by its sides. 17. A(5, 4), B(3, -1), C(7, -1) 18. A(-4, 1), B(5, 6), C(-3, -7) 19. A(-7, 9), B(-7, -1), C(4, -1) ...

... COORDINATE GEOMETRY Find the measures of the sides of ABC and classify each triangle by its sides. 17. A(5, 4), B(3, -1), C(7, -1) 18. A(-4, 1), B(5, 6), C(-3, -7) 19. A(-7, 9), B(-7, -1), C(4, -1) ...

Mathematics - Geometry

... being addressed in that particular quarter. The original intention of the boldface text was to show where in the balanced assessment piece that the standard would have been assessed. This can still be used as a guide for when students should begin to be accountable for the acquisition of that specif ...

... being addressed in that particular quarter. The original intention of the boldface text was to show where in the balanced assessment piece that the standard would have been assessed. This can still be used as a guide for when students should begin to be accountable for the acquisition of that specif ...

Greenwich Public Schools Mathematics Curriculum Objectives

... The measures of geometric figures can be calculated and analyzed using a variety of strategies, tools, and technologies. A change in one dimension of an object results in predictable changes in area and or ...

... The measures of geometric figures can be calculated and analyzed using a variety of strategies, tools, and technologies. A change in one dimension of an object results in predictable changes in area and or ...

Geometry

... iconic/pictorial, graphical, tabular, and symbolic), to solve problems, to model mathematical ideas, and to communicate solution strategies. CLE 3108.1.5 Recognize and use mathematical ideas and processes that arise in different settings, with an emphasis on formulating a problem in mathematical ter ...

... iconic/pictorial, graphical, tabular, and symbolic), to solve problems, to model mathematical ideas, and to communicate solution strategies. CLE 3108.1.5 Recognize and use mathematical ideas and processes that arise in different settings, with an emphasis on formulating a problem in mathematical ter ...

Geometry Common Core State Standards Regents at

... ABC onto triangle DEF? 1) a reflection over the x-axis followed by a reflection over the y-axis 2) a 180° rotation about the origin followed by a reflection over the line y = x 3) a 90° clockwise rotation about the origin followed by a reflection over the y-axis 4) a translation 8 units to the right ...

... ABC onto triangle DEF? 1) a reflection over the x-axis followed by a reflection over the y-axis 2) a 180° rotation about the origin followed by a reflection over the line y = x 3) a 90° clockwise rotation about the origin followed by a reflection over the y-axis 4) a translation 8 units to the right ...

# 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.