Define a perpendicular bisector, What does CPCTC stand for?, What are the ways to prove triangles congruent and the ways to prove triangles similar?, Define an altitude of a triangle ... Reasons used in Proofs. Coordinate Geometry. Preview; Assign Practice; Preview. It is formed by three or more line segments called sides. area = 10 2 sin(60°) which is also the same as. Diagonals bisect vertex angles. Case I. Special quadrilaterals include parallelograms, trapezoids, rectangles, rhombuses, and squares. We've seen that one of the properties of a rhombus is that its diagonals are perpendicular to each other. 9. Each side intersects exactly two sides, one at each endpoint, so that no two sides with a common endpoint are collinear. However, this doesn't sound correct to me. 0. prove it. Yolanda Hedtke. View Coord Geometry Proofs Packet _1613608322.pdf from GEOMETERY 101 at Central Piedmont Community College. This is the basic property of rhombus. How to prove a quadrilateral is a rhombus. Example. Misc. If point p(3,4)is equidistant from the point A (a+b,a-b) and B(a-b,a+ b) then prove that 3b-4a=0; Find the distance between the points (a cos 35°, 0)and (0, a cos 55°) Coordinate Geometry; Find the value of x; [The use of the set of axes below is optional.] Now let us find out the lengths of the diagonals of the rhombus. Find the area of rhombus. Related Topics Other topics in Quadrilaterals: Polygons; 0% average accuracy. cone圆锥. How Do You Write a Coordinate Proof? 4 Use coordinate geometry to prove that the diagonalsof an isosceles trapezoid are congruent. Coordinate Geometry. To prove a quadrilateral is a rhombus, here are three approaches: 1) Show that the shape is a parallelogram with equal length sides; 2) Show that the shape’s diagonals are each others’ perpendicular bisectors; or 3) Show that the shape’s diagonals bisect both pairs of … Examples: 1. Rhombus -> 4 equal sides. Find the distance of the point (-3, 4) from the x-axis. Nayana. The diagonals have the same midpoint, and one pair of opposite sides have equal lengths. A rhombus is a special kind of parallelogram, in which all the sides are equal. This tutorial shows you how to find the vertices of a rhombus that's graphed on the coordinate plane! We will check that the vectors AB and DC representing the pair of opposite. 3 minutes ago by . 0% average accuracy. Prove that a quadrilateral with the vertices A(-2,3), B(2,6), C(7,6) and D(3,3) is a rhombus. Here are the six ways to prove a quadrilateral is a parallelogram: Prove that opposite sides are congruent. The properties of various special quadrilaterals are proven using triangle congruence proofs. Let OABC be a rhombus such that OA is along x axis.Let BL and CM be prependiculars from B& C respectively on x-axis. To prove a quadrilateral is rhombus you must first prove the quadrilateral is a parallelogram (See how to prove a parallelogram above). ~ 4 ~ Lesson 7: Proving Special Quadrilaterals Standard: G.GPE.4: Use coordinates to prove simple geometric theorems algebraically.Standard: G.GPE.5: Prove the slope criteria for parallel and perpendicular lines; use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). Once again, they're corresponding sides of two congruent triangles, so they must have the same length. COORDINATE GEOMETRY. Definitions. Prove that is parallel to . Examples: 3. If two consecutive sides of a parallelogram are congruent, then it’s a rhombus (neither the reverse of the definition nor the converse of a property). `AC = sqrt((-3-2)^2 + (2 + 3))` `= sqrt((-5)^2 + (5)^2)` `= sqrt(25 + 25)` `= sqrt(50)` `AC = 5sqrt2` Answer. We have step-by-step solutions for your textbooks written by Bartleby experts! Prove that the quadrilateral with vertices A(-1,0), B(3,3), C(6,-1) … geometry. Prove that opposite sides are parallel. 5.有关立体图形. For point P, we have .And Why To use coordinate geometry to prove that a flag design includes a rhombus, as in Example 2 In Lesson 5-1, you learned about midsegments of triangles.A trapezoid also has a To solve this problem use coordinate geometry proof. Special quadrilaterals include parallelograms, trapezoids, rectangles, rhombuses, and squares. Right Triangles. In Euclidean geometry, a rhombus is a type of quadrilateral. Name: _ Coordinate Proofs: Rectangle, Rhombus, Square Period: _ Proving a Quadrilateral is a Rectangle Date: Angles. % Progress . 3 minutes ago by . It is just a quadrilateral and not one of the special ones mentioned above. If we can prove that any of the angles inside the figure is not a right angle, then this would show that \ ... A square is a rhombus where diagonals have equal lengths. Being as specific as possible, what type of figure is this? Three-Dimensional Shapes; V=lwh. prove a quadrilateral is a square. So BE is equal to DE. The properties of various special quadrilaterals are proven using triangle congruence proofs. rhombus菱形. In this article, we shall study to prove given quadrilateral to be or parallelogram, or rhombus, or square, or rectangle using slopes. regular solid/regular polyhedron正多面体. Since the diagonals of a rhombus are bisectors of eachother, and . Rectangle. Assign to Class. Click to see full answer. Multiply the length of the hypotenuse by four. P … Check it out! Write a plan to prove that the midpoints of the sides of a rhombus determine a rectangle using coordinate geometry. First, they prove that a figure with given points is another figure by using slopes.... Get Free Access See Review + 4:29. Find coordinate geometry rhombus lesson plans and teaching resources. If the diagonals … Ex. Ex. Be sure to include the formulas* Coordinate geometry formulas. Prove it is a rhombus for any values of a and b. I have tried to solve this by saying that since points A and C both have equal x and y coordinates, that this means all 4 sides are equal etc. Gravity. The shape of a rhombus is in a diamond shape. *Write a plan to prove that the midpoints of the sides of a rhombus determine a rectangle using coordinate geometry. How Do You Write a Coordinate Proof? circular cylinder圆柱体. Analytical geometry, also referred to as coordinate or Cartesian geometry, is the study of geometric properties and relationships between points, lines and angles in the Cartesian plane. (Coordinate Geometry) A quadrilateral where all interior angles are 90°, and whose location on the coordinate plane is determined by the coordinates of the four vertices (corners). Square … To prove a quadrilateral is a rhombus, here are three approaches: 1) Show that the shape is a parallelogram with equal length sides; 2) Show that the shape’s diagonals are each others’ perpendicular bisectors; or 3) Show that the shape’s diagonals bisect both pairs of … The coordinates for a rhombus are given as (2a, 0) (0, 2b), (-2a, 0), and (0.-2b). How do you write a plan to prove that the midpoints of the sides of a rhombus determine a rectangle using coordinate geometry? | Socratic Quadrilateral ABCD has points A (0,0) B (a,b) C (a+b,a+b) D (b,a). In geometry, a figure that lies in a plane is called a plane figure. So this is corresponding sides of congruent triangles. Quickly find that inspire student learning. Answers: 1 on a question: The coordinates for a rhombus are given as (2a, 0), (0, 2b), (–2a, 0), and (0, –2b). Proofs for Rhombuses - Video & Lesson Transcript | Study.com The coordinates for a rhombus are given as (2a, 0), (0, 2b), (-2a, 0), and (0,-2b), Write a plan to prove that the midpoints of the sides of a rhombus determine a rectangle using coordinate geometry. Additionally, theorems involving the midpoints of the sides of a triangle are also explored. This is the basic property of rhombus. Check lines of symmetry in a rhombus. Distance between two points. Opposite sides have congruent slopes. To find the y-intercept, set x equal to 0 and solve for y. 0. Prove that opposite angles are congruent. 9. Ex. Rhombus. - Show that both pairs of opposite sides are parallel. Write. Coordinate Geometry; The geometry rules concerning slope are very important to remember. Coordinate Geometry. Different forms equations of straight lines. 6 Use coordinate geometry to prove the quadrilateral isa parallelogram. 1. prove that the line segment joining the midpoints of the sides of a rectangle form a rhombus We saw some very simple problems involving the distance formula, and a few applications involving triangles and quadrilaterals. Yolanda Hedtke. QUIZ NEW SUPER DRAFT. (a,b). A coordinate proof is used in geometric theorems as proof to make ‘generalized’ arguments in cartesian planes. trapezoid梯形. Prove that consecutive angles are supplementary (adding to 180°) Prove that an angle is supplementary to both its consecutive angles. • Make a conjecture and identify and execute appropriate strategy to classify a quadrilateral on the coordinate plane. (2012OD) Solution: B(-3, 0), A (-3, 4) Question 2. arc弧. • Analyze given information to prove if a quadrilateral is a parallelogram, rectangle, rhombus, or square. Point of intersection. rectangular solid长方体. Their four ends must form a diamond shape — a rhombus. Coordinate Geometry . prove a quadrilateral is a rhombus. COORDINATE GEOMETRY. -1 Therefore, a rhombus is a parallelogram. h {\displaystyle h} into the formula for the perimeter of a rhombus, which … If Polar Coordinates of A is and B is then distance between A nd B.. AB = Now we will learn different applications of distance formula. Only use one setof sides. cube立方体，立方数. To prove it is rhombus, we can prove any one of the following. To do this, you will need to do the distance formula 4 times. Click card to … Any ideas? Area of the Rhombus = (a * b)/ 2. 5 Use coordinate geometry to prove that the diagonalsof a rhombus are perpendicular. Ex. Prove it is a rhombus for any values of a and b. I have tried to solve this by saying that since points A and C both have equal x and y coordinates, that this means all 4 sides are equal etc. Additionally, theorems involving the midpoints of the sides of a triangle are also explored. In this tutorial, you'll see how to write a coordinate proof to prove that two triangles are congruent. Identify and calculate area of shapes based on coordinates on a plane. Ask Question Asked 4 years, 11 months ago. Be sure to include the . There are several theorems related to the study of circles and their properties. see explanation. d) prove that ∆ RBH ( ∆OBM (again, using coordinate geometry) 3. This indicates how strong in your memory this concept is. In rhombus , is the point at which the diagonals intersect. The coordinates for a rhombus are given as (2a, 0), (0, 2b), (–2a, 0), and (0, –2b). This 7 lesson unit contains lessons on quadrilaterals. h {\displaystyle h} into the formula for the perimeter of a rhombus, which is. GEOMETRY COORDINATE GEOMETRY Proofs Name _ Period _ 1 Coordinate Proof Help Page Formulas Slope: Distance: √ To show segments ... geometry - quadrilateral coordinate proofs. Method 2: Prove that a pair of adjacent sides are equal. Parallelogram – a quadrilateral with both pairs of opposites sides parallel. Notice that we proved three points to be collinear (and others geometric results) by using only algebraic expressions and equations. Solution. Method: First, prove the quadrilateral is a rhombus by showing all four sides is congruent; then prove the quadrilateral is a rectangle by showing the diagonals is congruent. Check it out! Show all work. Answer. Quadrilateral Classification in the Coordinate Plane. Coordinate geometry with proofs. The surface area is simply the sum of the areas of the six rectangular faces. SA=2lw+2wh+2lh. Because the sides of a rhombus … How do you prove a rhombus in coordinate geometry? parallelogram 2. rhombus 3. quadrilateral 4. rectangle Geometry Martin wants to use coordinate geometry to prove that the opposite sides of a rectangle are congruent. Click Create Assignment to assign this modality to your LMS. Coordinate Geometry Proofs #2 Name:_____ Period:_____ Date:_____-- 1) Triangle TRI has vertices T(15,6), R(5,1), and I(5,11). STUDY. Then demonstrate that all the sides are congruent. Slope formula 4 times. In a rhombus with sides of 10 yards and interior adjacent angles of 60° and 120° then to find the area of this rhombus, we would plug this into our formula for area using the side and an angle. 1) If P (-2,1), L (2,-7), A (4,-1), and Y (-4-5), prove that line segments PL and AY are perpendicular bisectors of each other. Geometry; Add to your collection Add the current resource to your resource collection. Maps Practical Geometry Separation of Substances Playing With Numbers India: Climate, Vegetation and Wildlife class 7 Inside Our Earth Perimeter and Area Winds, Storms and Cyclones Struggles for Equality The Triangle and Its Properties Properties of Parallelograms. The origin is the midpoint of that diagonal. Trapezoid -> Exactly 1 pair of parallel sides. Coordinate geometry with proofs. The shape of a rhombus is in a diamond shape. Proofs Using Coordinate Geometry 348 Chapter 6 Quadrilaterals What You’ll Learn • To prove theorems using figures in the coordinate plane. This geometry video tutorial explains how to prove if a parallelogram is also a rhombus using two column proofs. Step 1. Prove it is a Rectangle. The coordinate geometry proofs require a thorough understanding of the properties of several geometric shapes, such as triangles, rhombus, quadrilaterals, and other polygons. Point of intersection. Maths . Proof that the diagonals of a rhombus divide it into 4 congruent triangles. Define a perpendicular bisector. 4.其它平面图形. Supplementary angles add up to 180 degrees. parallel lines平行线. Name_ Coordinate Geometry Proofs USE COORDINATE GEOMETRY TO DO YOUR PROOFS FOR ALL PROBLEMS In Triangle PBQ By Pythagoras Theorem PQ = . 2) Two students are debating over how to prove that a quadrilateral is a rhombus. 5 Use coordinate geometry to prove that the diagonalsof a rhombus are perpendicular. Some of the properties of a rhombus : 1) all sides are congruent, => AB=BC=CD=DA, 2) opposite angles are congruent, => angleADC=angleABC=y, and angleBAD=angleBCD=x, 3) adjacent angles are supplementary, => x+y=180^@ 4) opposite sides are parallel, => AD // BC, and AB // DC, given that P,Q, R and S are midpoints of AB,BC,CD, … 9th - 10th grade . Play this game to review Geometry. We have a new and improved read on this topic. Try this Drag any vertex of the rectangle below. now prove that RHOM is a rhombus. Position of Three Points:- Learn vocabulary, terms, and more with flashcards, games, and other study tools. Here we will show the converse- that if a parallelogram has perpendicular diagonals, it is a rhombus - all its sides are equal. Lines. That if we know the lengths of the diagonals, the area of the rhombus is 1/2 times the products of the lengths of the diagonals, which is kind of a neat result. Write a plan to prove that the midpoints of the sides of a rhombus determine a rectangle using coordinate geometry. Be sure to include the formulas. 3. Slope formula 2 twice. Step 2: Prove that the figure is a parallelogram. How do I prove analytically using co- ordinate geometry that the diagonals of a rhombus are perpendicular to each other Ask Question Asked 4 years, 7 months ago Only use one setof sides. ... is a rhombus. Match. Flashcards. Different forms equations of straight lines. segment of a circle弧形. And Coordinate Geometry Answers question is a coordinate geometry question. Quadrilateral -> 4 sided figure. Write a plan to prove that the midpoints of the sides of a rhombus determine a rectangle using coordinate geometry. Ex. Practice. When the bigger and smaller diagonals of a rhombus are given and equal to D and d, respectively, the side of a rhombus equals sqrt ( (d/2)^2 + (D/2)^2). Mathematics. Hence, it is also called a diamond. 100. prove diagonals perpendicular and opposite sides parallel. Let P, Q and R be the three points which divide the line-segment joining the points A(-2, 2) and B(2, 8) in four equal parts. Prove a quadrilateral with 4 rt. This one is a medium level difficulty question and tests the following concepts: finding length of a line segment given coordinates of its end points; properties of quadrilaterals including square, rectangle, rhombus ... Quadrilateral properties. In Euclidean geometry, a rhombus is a type of quadrilateral. Preview this quiz on Quizizz. Rhombus. Test. Geometry. Hence, it is also called a diamond. 21CT expand_more High School Math Geometry McDougal Littell Jurgensen Geometry: Student Edition Geometry To prove: The segments joining the midpoints of consecutive sides of a rectangle form a rhombus. Use coordinate geometry to prove the quadrilateral is a parallelogram. And we've done our proof. The slope of AB = 4/3. Example – 01: Using slopes show that the points (-2, -1), (4, 0), (3, 3) and (-3, 2) are the vertices of a parallelogram. 8:06 The equation of a straight line, given … Circles are important in mathematics since they form a huge part of the geometry syllabus. This 7 lesson unit contains lessons on quadrilaterals. If Coordinate of Point P = (x 1,y 1) and Coordinate of Point Q = (x 2,y 2). Answer (1 of 3): First off, pick a coordinate system so that one of the diagonals of the rhombus lies on the x-axis, so that two opposite corners have coordinates (-a,0), (a,0). Let midpoints of AB be P and its coordinates are ((2a+0)/2,(0+2b)/2) i.e. Then we looked at some of the important theorems related to rhombuses and also saw the proofs for them. Opposite angles in the rhombus are equal. The diagonals of the rhombus bisect each other and are perpendicular to each other. The diagonals of the rhombus bisect the vertex angles. Be sure to include the . Since the hypotenuse is also the side of the rhombus, to find the perimeter of the rhombus, you need to plug the value of. 0 plays. Prove that quadrilateral MATH is a parallelogram. A (0, -3), B (-4, 0), C (2, 8), D (6, 5) Step 1: Plot the points to get a visual idea of what you are working with. If the quadrilateral is a rhombus one of whose angles is a right angle, then it is a square. Coordinate Geometry 8 200 Negative gradients: m < 0 Positive gradients: m > 0 Chapter Contents 8:01 The distance between two points 8:02 The midpoint of an interval 8:03 The gradient of a line 8:04 Graphing straight lines 8:05 The gradient–intercept form of a straight line: y = mx + c Investigation: What does y = mx + c tell us? Since the hypotenuse is also the side of the rhombus, to find the perimeter of the rhombus, you need to plug the value of. Mathematics. Ex. In the last three of these methods, you first have to prove (or be given) that the quadrilateral is a rectangle, rhombus, or both: If a quadrilateral has four congruent sides and four right angles, then it’s a square (reverse of the square definition). In this tutorial, you'll see how to write a coordinate proof to prove that two triangles are congruent. MEMORY METER. Related Topics Other topics in Quadrilaterals: Polygons; How do you prove a rhombus in coordinate geometry? The one main way to prove that a quadrilateral is a rhombus is to prove that the distances of the four sides of the quadrilaterals are congruent (equal distances) and then prove that the diagonals of the quadrilateral are not congruent (unequal distances). Click to see full answer. G.G.69: Quadrilaterals in the Coordinate Plane 2 www.jmap.org 1 G.G.69: Quadrilaterals in the Coordinate Plane 2: Investigate the properties of quadrilaterals in the coordinate plane, using the distance, midpoint, and slope formulas 1 The coordinates of quadrilateral PRAT are , , , and . The one main way to prove that a quadrilateral is a rhombus is to prove that the distances of the four sides of the quadrilaterals are congruent (equal distances) and then prove that the diagonals of the quadrilateral are not congruent (unequal distances). Parallelogram -> 2 pairs of parallel sides. Rectangle -> 4 right angles. Rhombus. 0 plays. PLAY. Preview this quiz on Quizizz. Spell. Graph the rhombus with vertices A(2, 2),B(7, 2),C(4, -2), and D(-1, -2). Then, connect the midpoints of consecutive sides to form a quadrilateral. What do you notice about the quadrilateral? The quad. is a rectangle. AlgebraGive the coordinates of Bwithout using any new variables. 2. rectangle3.isosceles triangle Prove that a shape must be a rhombus using rules of coordinate geometry. This is what coordinate geometry is all about ! - Show that both pairs of opposite sides are congruent. G.GPE.B.4: Quadrilaterals in the Coordinate Plane 2 www.jmap.org 3 9 The vertices of quadrilateral MATH have coordinates M(−4,2), A(−1,−3), T(9,3), and H(6,8). A polygon is a closed plane figure with the following properties. 21CT expand_more High School Math Geometry McDougal Littell Jurgensen Geometry: Student Edition Geometry To prove: The segments joining the midpoints of consecutive sides of a rectangle form a rhombus. Progress % Practice Now. angles.Slope formula 4 times. Be sure to include the formulas. Square – a parallelogram with four congruent sides and four right angles. Similarly midpoint of BC is Q(-a,b); midpoint of CD is R(-a,-b) and midpoint of DA is S(a,-b). geometry. There are 5 different ways to prove that this shape is a parallelogram. 2. To prove it is rhombus, we can prove any one of the following. If the quadrilateral is a rhombus with congruent diagonals, then it is a square. 1. sphere球体. Important Questions for Class 10 Maths Chapter 7 Coordinate Geometry Coordinate Geometry Class 10 Important Questions Very Short Answer (1 Mark) Question 1. This tutorial shows you how to find the vertices of a rhombus that's graphed on the coordinate plane! Use the slope formula. Let the points of rhombus be A(2a, 0), B(0, 2b), C(-2a, 0) and D(0.-2b). It's essentially base times height, but for a rhombus we could do that because it is a parallelogram, but we also have this other neat little result that we proved in this video. ... 10th graders solve and draw 10 different problems related to complete proofs in coordinate geometry. It is a special case of a parallelogram, whose all sides are equal and diagonals intersect each other at 90 degrees. Quadrilateral – four-sided figure. Method 3: Prove that all four sides are equal. Prove that quadrilateral MATH is a rectangle. ... ToProve : if the diagonals of parallelograms are perpendicular, then the parallelogram is a rhombus.. close. line,straight line直线. 9th - 10th grade . Coordinate Page 5/25 slope formula. Nov 8, 2014. Use coordinate geometry to prove that triangle TRI is isosceles. Coordinate Geometry 8 200 Negative gradients: m < 0 Positive gradients: m > 0 Chapter Contents 8:01 The distance between two points 8:02 The midpoint of an interval 8:03 The gradient of a line 8:04 Graphing straight lines 8:05 The gradient–intercept form of a straight line: y = mx + c Investigation: What does y = mx + c tell us? View Coordinate+Proofs (1).pdf from MATH 699 at College of Charleston. Coordinate geometry formulas. It will remain a rectangle and its dimensions calculated from its coordinates. geometry. • Explain correspondences between formulas and important features of polygons. Clearly, triangles ABL & OCM are congruent. Thinking about Geometry. The slope of a line = rise/run to establish that opposite sides are parallel. 8:06 The equation of a straight line, given … Proving a Quadrilateral is a Rhombus Prove that it is a parallelogram first, then: Method 1: Prove that the diagonals are perpendicular. QUIZ NEW SUPER DRAFT. what is the area of a rhombus with a 60 degree angle and sides 5 cm long? Step 2. Multiply the length of the hypotenuse by four. A guide to proving different types of quadrilaterals using coordinate geometry: 3. Class-X . b) Prove that (2,2) is a point on both diagonals of the quadrilateral. Play this game to review Geometry. 6 Use coordinate geometry to prove the quadrilateral isa parallelogram. 22 4. There are several formulas for the rhombus that have to do with its: Sides (click for more detail) All 4 sides are congruent. area = 10 2 sin(120°) Then, we multiply these two numbers together: area = 100 × 0.866. We've shown that, look, diagonal DB is splitting AC into two segments of equal length and vice versa. 2. There are 5 different ways to prove that this shape is a parallelogram. Geometrical shapes are defined using a coordinate system and algebraic principles. Chapter 4: Analytical geometry. find the coordinates of B (do so by finding equations for and and solving the system of 2 equations) give another way to do problem b) and explain. Textbook solution for McDougal Littell Jurgensen Geometry: Student Edition… 5th Edition Ray C. Jurgensen Chapter 5.4 Problem 34WE. Prove that the quadrilateral ABCD with the vertices in a coordinate plane. If either diagonal of a parallelogram bisects two angles, then it’s a rhombus (neither the reverse of the definition nor the converse of a property). . The same can be done for the other two sides, and know we know that opposite sides are parallel. ~ 4 ~ Lesson 7: Proving Special Quadrilaterals Standard: G.GPE.4: Use coordinates to prove simple geometric theorems algebraically.Standard: G.GPE.5: Prove the slope criteria for parallel and perpendicular lines; use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). Choose one of the methods. Distance between two points. The coordinates for a rhombus are given as (2a, 0), (0, 2b), (–2a, 0), and (0, –2b). Rhombus – a parallelogram with four congruent sides. Using a coordinate geometry proof and a geometric proof 4 Use coordinate geometry to prove that the diagonalsof an isosceles trapezoid are congruent. Diagonals. View Coordinate Geometry Proofs.pdf from MISC 11XB at Bronx High School of Science. Find the area of rhombus. Example: Prove that the following four points will form a rectangle when connected in order. Perimeter = 4 *length of side. line segment线段. It is a special case of a parallelogram, whose all sides are equal and diagonals intersect each other at 90 degrees. Check lines of symmetry in a rhombus. The coordinates for a rhombus are given as (2a, 0), (0, 2b), (–2a, 0), and (0, –2b). Hence we have proved that the quadrilateral formed by the given four vertices is a rhombus.
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