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what are the properties of the quadrilateral whose vertices are the center of the squares?

The sides of a parallelogram are sides of four squares drawn outside the parallelogram , Give some properties of the quadrilateral whose vertices are the center of these four squares?

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Quadrilaterals - Square, Rectangle, Rhombus, Trapezoid ...


Quadrilaterals. Quadrilateral just ... (Also see this on Interactive Quadrilaterals) Properties. Four sides (edges) Four vertices (corners) ... NOTE: Squares, ...
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Quadrilateral - Wikipedia


A quadrilateral is a square if and only if it ... A quadric quadrilateral is a convex quadrilateral whose four vertices all lie on ... Properties of the ...
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Shape: Quadrilateral | Think Math!


... or vertices have special properties. ... squares (B), the most special of ... any quadrilateral whose opposite angles add up to 180 degrees is a cyclic quadrilateral.
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Square - Wikipedia


The perimeter of a square whose four ... a square is the quadrilateral containing ... (squares in its interior such that all four of a square's vertices lie on ...
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The sides of a parallelogram are sides of four squares drawn ...


... squares drawn outside the parallelogram. Give some properties of the quadrilateral whose vertices are the center ... vertices are the center of these four squares?
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Properties of Shapes: Quadrilaterals, Parallelograms ...


Properties of Shapes: Rectangles, Squares and Rhombuses ... they also have four vertices, or corners. ... Properties of Shapes: Quadrilaterals, Parallelograms, ...
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Geometry parallelograms Flashcards | Quizlet


Geometry parallelograms. STUDY. PLAY. ... angles whose vertices are not consecutive. ... Quadrilateral (3 properties) 1. Has 4 sides 2.
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Properties of Shapes: Quadrilaterals, Parallelograms ...


What is a Quadrilateral? - Definition, Properties, ... they also have four vertices, ... Properties of Shapes: Quadrilaterals, Parallelograms, Trapezoids, ...
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Square and its properties. (Coordinate Geometry) - Math Open ...


Definiton and properties of a square (coordinate geometry ... In coordinate geometry, ... The length of a diagonals is the distance between any pair of opposite vertices.
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Classification of Quadrilaterals - Cut-the-Knot


Classification of Quadrilaterals. ... by relaxing its properties. A square is a quadrilateral with all sides ... the vertices and the sides of the quadrilateral.
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Suggested Questions And Answer :


what are the properties of the quadrilateral whose vertices are the center of the squares?

The quadrilateral so formed is a rhombus (a parallelogram in which all the sides are of equal length). The interior angles of the rhombus are 90+x and 90-x where x is the angle of the parallelogram and where 90+x are the measures of opposite angles of the rhombus. The adjacent angles add up to 180, and 90+x+90-x=180. Call the parallelogram ABCD and let angle BAD be x. Because opposite side and opposite angles of a parallelogram are equal, we only need to consider two sides. Let AB=a and AD=b be two adjacent sides. Let the bisectors of these sides be points P and Q respectively. AP=PB=a/2 and AQ=QD=b/2. Outside ABCD, draw XP, length a/2, perpendicular to AB, and YQ, length b/2, perpendicular to AD. X and Y are the centres of the squares on AB and AD. One side of the new quadrilateral is defined by the line XY. So let's find its length. AX=a/sqrt(2) and AY=b/sqrt(2), because they are hypotenuses of triangles AXP and AYQ. XY=a^2/2+b^2/2-abcosXAY (cosine rule). Angle XAY=XAP+BAD+QAY=45+x+45=90+x. cosXAY=cos(90+x)=-sinx. So XY=a^2/2+b^2/2+absinx. Let's find the length of an adjacent side of the new quadrilateral. This time we have angle CDA=180-x. CD is bisected at R and WR is the perpendicular on to CD, and WR=RD=RC=a/2 because DC is parallel and equal in length to AB. Angle YDW=360-(RDW+180-x+QDY)=360-(45+180-x+45)=90+x, and cos(90+x)=-sinx. WY=DW^2+DY^2-2DWDYcosYDW=a^2/2+b^2/2+absinx. Therefore WY=XY. Since there is symmetry in the geometry the other two sides will be the same. And the opposite interior angles are equal. Therefore we have rhombus. When you draw the diagram you may find that XY is exterior to the parallelogram, and WY is interior. Nevertheless, since sin(180-x)=sinx, the lengths of the sides will still be equal. There are various other geometries that may apply, but you will find that you always get a combination of two angles of 45 degrees and the angle of the parallelogram (skew), but sinx will always be the result (for example, cos(90-x)=sinx, cos(45-x+45)=sin(x), cos(180-(90+x))=sinx, etc.).
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If you know a figure has certain properties, can you say what kind of figure it is?

The properties have to be sufficient to define the figure unambiguously, so that no other figure has those properties. For example, a quadrilateral with sides of equal length does not define a square, because a rhombus has the same properties. But a regular quadrilateral has equal length sides and angles, so a square is so defined.
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Discuss at least three applications of graph theory in the field of computer sciences?

Graphs are among the most ubiquitous models of both natural and human-made structures. They can be used to model many types of relations and process dynamics in physical, biological[1] and social systems. Many problems of practical interest can be represented by graphs. In computer science, graphs are used to represent networks of communication, data organization, computational devices, the flow of computation, etc. One practical example: The link structure of a website could be represented by a directed graph. The vertices are the web pages available at the website and a directed edge from page A to page B exists if and only if A contains a link to B. A similar approach can be taken to problems in travel, biology, computer chip design, and many other fields. The development of algorithms to handle graphs is therefore of major interest in computer science. There, the transformation of graphs is often formalized and represented by graph rewrite systems. They are either directly used or properties of the rewrite systems (e.g. confluence) are studied. Complementary to graph transformation systems focussing on rule-based in-memory manipulation of graphs are graph databases geared towards transaction-safe, persistent storing and querying of graph-structured data. Graph-theoretic methods, in various forms, have proven particularly useful in linguistics, since natural language often lends itself well to discrete structure. Traditionally, syntax and compositional semantics follow tree-based structures, whose expressive power lies in the Principle of Compositionality, modeled in a hierarchical graph. More contemporary approaches such as Head-driven phrase structure grammar (HPSG) model syntactic constructions via the unification of typed feature structures, which are directed acyclic graphs. Within lexical semantics, especially as applied to computers, modeling word meaning is easier when a given word is understood in terms of related words; semantic networks are therefore important in computational linguistics. Still other methods in phonology (e.g. Optimality Theory, which uses lattice graphs) and morphology (e.g. finite-state morphology, using finite-state transducers) are common in the analysis of language as a graph. Indeed, the usefulness of this area of mathematics to linguistics has borne organizations such as TextGraphs, as well as various 'Net' projects, such as WordNet, VerbNet, and others. Graph theory is also used to study molecules in chemistry and physics. In condensed matter physics, the three dimensional structure of complicated simulated atomic structures can be studied quantitatively by gathering statistics on graph-theoretic properties related to the topology of the atoms. For example, Franzblau's shortest-path (SP) rings. In chemistry a graph makes a natural model for a molecule, where vertices represent atoms and edges bonds. This approach is especially used in computer processing of molecular structures, ranging from chemical editors to database searching. In statistical physics, graphs can represent local connections between interacting parts of a system, as well as the dynamics of a physical process on such systems. Graph theory is also widely used in sociology as a way, for example, to measure actors' prestige or to explore diffusion mechanisms, notably through the use of social network analysis software. Under the umbrella of Social Network graphs there are many different types of graphs: Starting with the Acquaintanceship and Friendship Graphs, these graphs are useful for representing whether n people know each other. next there is the influence graph. This graph is used to model whether certain people can influence the behavior of others. Finally there's a collaboration graph which models whether two people work together in a particular way. The measure of an actors' prestige mentioned above is an example of this, other popular examples include the Erdős number and Six Degrees Of Separation Likewise, graph theory is useful in biology and conservation efforts where a vertex can represent regions where certain species exist (or habitats) and the edges represent migration paths, or movement between the regions. This information is important when looking at breeding patterns or tracking the spread of disease, parasites or how changes to the movement can affect other species. In mathematics, graphs are useful in geometry and certain parts of topology, e.g. Knot Theory. Algebraic graph theory has close links with group theory. A graph structure can be extended by assigning a weight to each edge of the graph. Graphs with weights, or weighted graphs, are used to represent structures in which pairwise connections have some numerical values. For example if a graph represents a road network, the weights could represent the length of each road. A digraph with weighted edges in the context of graph theory is called a network. Network analysis have many practical applications, for example, to model and analyze traffic networks. Applications of network analysis split broadly into three categories: First, analysis to determine structural properties of a network, such as the distribution of vertex degrees and the diameter of the graph. A vast number of graph measures exist, and the production of useful ones for various domains remains an active area of research. Second, analysis to find a measurable quantity within the network, for example, for a transportation network, the level of vehicular flow within any portion of it. Third, analysis of dynamical properties of networks.
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how do you find the area of a prism???

All prisms take a two-dimensional shape and use it as the top and bottom faces in parallel. The top and bottom are then joined to make a solid, so that all the sides are parallelograms. These parallelograms can be rectangles or even squares. The area of the prism is the surface area of the solid, usually including the top and bottom surfaces. The top and bottom faces can each be the same triangle, quadrilateral (including squares, rectangles, trapezoids, etc.), or polygon (star, pentagon, hexagon, etc.). If the top and bottom have n sides, there will be n parallelograms forming the length of the prism. The area of each parallelogram is base times vertical height, where the base length is the length of the particular side of the base figure on which the parallelogram stands. The volume of the prism is the area of the base times the vertical height. For example, if the top and bottom faces are the same regular hexagon (like a pencil), there will be 6 rectangles forming the sides of the prism, each with the same area, A. The surface area of the prism is 6A plus twice the area of the base, or bottom face.
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Mapping from three to two dimensions

The coordinates of the four points can be calculated as follows:  
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how to graph the parabola for f(x)=x^2-5x-14

f(x)=x^2-5x-14 can be written f(x)=x^2-5x+25/4-25/4-56/4=(x-5/2)^2-81/4. This "completes the square". How did I do this? I looked at x^2-5x and asked myself: what do I need to add to this to complete the square involving x? What you do is halve the x term, 5, and then square it: (5/2)^2=25/4. Now I have the complete square of x-5/2. But I have to compensate for adding in 25/4 so I do this by subtracting -25/4, but keep this separate from the perfect square and absorb it into the number -14. I can represent -14 as an improper fraction -56/4 in a convenient form to combine with -25/4 so that -25/4-56/4=-81/4 is the combined result. Now f(x)=(x-5/2)^2-(9/2)^2, and some of the properties of the parabola can be more easily seen. The graph is U-shaped and cuts the x axis at the zeroes for the function. To find these intercepts, we put (x-5/2)^2-(9/2)^2=0 so (x-5/2)^2=(9/2)^2 and taking square roots of each side we get: x-5/2=+9/2, from which x=5/2+9/2 and x=7 or -2 (also f(x)=(x-7)(x+2)). These are x intercepts and halfway between them at  x=5/2 (1/2 of 7+(-2)) and y=-81/4 is the vertex (in this case the lowest point with x=5/2 as the vertical axis of symmetry). This makes it easy to visualise and draw the graph. We can also work out the y intercept, when x=0. This is -14. All the points labelled fix the symmetrical parabola into position. The arms of the U spread apart and you can plot various values away from the zeroes to see what the spread is.
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explain complex number and vectors

Start with real numbers. A number line is often used to represent all real numbers. It has infinite length and somewhere we can mark zero, dividing positive numbers (on the right of zero) and negative numbers (on the left of zero). The line is continuous so no real number can be left out. A line is 1-dimensional. A complex number has two components: one real, the other imaginary. A complex number can be represented by a plane, and it's 2-dimensional. So what does imaginary mean? The basis of imaginary numbers is the square root of minus one (sqrt(-1)) and traditionally it is given the symbol i. The square root of any negative number can be expressed using i. So, for example, the square root of minus 4 is 2i, because -4=4*-1 and the square root of 4*-1 is 2sqrt(-1)=2i. A complex number, z, can be written a+ib, where a and b are real numbers. But, more importantly perhaps, they can be represented as a point in 2-dimensional space as the point (a,b) plotted on a graph using the familiar x-y coordinate system. So, just like the number line represented all real numbers like an x axis, so all complex numbers can be represented by a plane, an infinite x-y plane. Now we come to vectors. There is a commonality between complex numbers and vectors. A straight road with cars , houses, people, etc., on it make the road like a number line. Any position on the road can be related to a fixed point on the road we'll call "home". Objects to the right, or eastward, could be in front of home and those to the left, or westward, behind home. The position of an object is the distance from home. This is a 1-dimensional vector field, where all objects have position. If the objects move their speed will have direction, towards the right or towards the left and we can say that a speed to the right is positive and a speed to the left is negative. Now we introduce another straight road at right angles to the first road. Now the picture is 2-dimensional. The position of an object is defined by two values: position east or west and position north or south. North can be positive and south negative. This is equivalent to the complex plane, which represents all complex numbers. The 2-dimensional plane represents all 2-dimensional vectors, whether it's position or speed. But the word "velocity" is used instead of "speed", because velocity includes direction, but speed is just a number, or magnitude, of the velocity. A vector has an east-west (EW) component (x value) and a north-south (NS) component (y value) and a vector r=xi+yj, where i is called a unit vector in the NS direction and j in the EW direction, so the point (x,y) fixes the positional vector r. Vectors are usually written in bold type, so you won't confuse i with i. The magnitude of a vector is sqrt(x^2+y^2) so it is represented by the hypotenuse of a right-angled triangle whose other sides are x and y. Pythagoras' theorem is used to work out the value. The magnitude of a vector is sometimes written |r| and is called a "scalar" quantity, so it doesn't have a direction or a sign (positive or negative), because the sign is a property of the direction of the vector.  A vector is not limited to a 2-dimensional plane. It can have as many dimensions as necessary. An aeroplane's positional vector and velocity would involve another dimension: height. A submarine's positional vector and velocity would involve depth. Height and depth are perpendicular to the EWNS plane and together form 3-dimensional space. The unit vector for height and depth is k, and height would be positive while depth would be negative, and the letter z is used with x and y so that a point in 3-space is (x, y, z). The magnitude |r| is sqrt(x^2+y^2+z^2). When working with vectors, addition and subtraction requires adding and subtracting the x, y, z components separately. When adding or subtracting complex numbers, the same applies to the x and y, real and complex, components. Multiplication and division are a special topic beyond the scope of this introductory explanation.  
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find the dimensions of the rectangle with the largest area that can be inscribed in a semi-circle with a radius of 4

A parallelogram inscribed in a circle is a rectangle or a square.   The perpendicular bisector of two opposite sides of the rectangle corresponds to a diameter of the circle. So, a rectangle inscribed in a semicircle rests on the diameter. ( Proving things mentioned above is skipped in here.) Label each vertex of the rectangle A, B, C and D counterclockwise as placing base AB on the diameter and vertices C and D on the circumference. The midpoint of AB corresponds to the circle's center O. Let angle∠AOD=x (0 Read More: ...

what two-dimensional figure has the same number of vertices as a trapezoid?

A rhombus, kite, quadrilateral, square, rectangle, parallelogram all have four vertices.
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how do find the size of sides in an octogon, when nothing is given?

how do find the size of sides in an octogon, when nothing is given? the size of the piece is 2.250x2.250. There are eight vertices in an octagon, so there are eight internal angles from the center to the vertices. Each angle is three hundred sixty degrees divided by eight, or forty-five degrees. We can use the tangent of half that angle to find the length of one half of a side of the octagon (as shown in the figure). The base of the angle is one half of the square that encloses the octagon. x / 1.125 = tan 22.5 x / 1.125 = 0.414213 x = 0.414213 * 1.125 x = 0.46599 The length of the side is twice that. s = 2 * x s = 2 * 0.46599 s = 0.93198
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