Prove that the diagonals of any parallelogram bisect each other. (Hint: Label three of the vertices of the parallelogram O(0, 0), A(a, b), and C(0, c).)

Q: Every rectangle is a parallelogram. O True OFalse

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Q: Determine whether the planes 2x - 3y + 6z = 12 and 6x + 8y + 2z = 1 are parallel, orthogonal, or…

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Q: The parallelogram (ABCD) has vertices at A(2,-1,4), B(1,0, –1), C(1, 2, 3), and D, then اخترأحد…

A: We have to find Coordinate D, Area of parallelogram and projection of BC onto BA.

Q: The vertices of quadrilateral JOHN are J(-3,1), O(3,3), H(5,7), and N(-1,5). Use coordinate geometry…

A: We are given the vertices J(-3, 1), O(3, 3), H(5, 7), and N(-1, 5). Let us plot the graph first.

Q: The parallelogram (ABCD) has vertices at A(2, -1, 4), B(1,0,-1), C(1,2,3), and D, then اخترأحد…

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Q: 6. Show that the diagonals of the square with the given vertices are congruent perpendicular…

A: The formula for the midpoints of (x1,y1) and (x2,y2) is x2+x12,  y2+y12 and the formula for the…

Q: 2. Let D be the parallelogram in R? whose vertices are (0,0), (1, 1), (2, –1) and (3,0). By substi-…

A: We have to the value of integral.

Q: e of the parallelepiped with the given vertices A, B, C and

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Q: Verify that the points are the vertices of a parallelogram, and find its area. A(1, 1, 3), B(-2, -6,…

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Q: 1. Rhombus ABCD with vertices A(-3, -2), B(0, 3), C(5, 6), and D(2, 1): (x, y)- (x+2, y-6)

A: In Rhombus, A=(-3,-2)B=(0,3)C=(5,6)D=(2,1)

Q: The parallelogram (ABCD) has vertices at A(2,-1, 4), B(1,0, -1).C(1,2,3), and D, then

A: Let A(2,-1,4) , B(1,0,-1) , C( 1,2,3) and D(x,y,z) Let AC be one diagonal and BD be another…

Q: The parallelogram (ABCD) has vertices at A(2,-1, 4), B(1,0,-1), C(1,2, 3), and D, then اخترأحد…

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Q: Prove a quadrilateral with vertices G(1,1), H(5,3), I(4,5) and J(0,3) is a rectangle

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Q: Prove that if DABCD is a parallelogram, then DABCD is convex.

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Q: Prove that the diagonals of a rectangle are of equal length. [Hint: Take the vertices of the…

A: To prove that diagonals of a rectangle are if equal length.  Consider a rectangle which has one…

Q: A parallelogram is a rhombus if and only if the diagonals are perpendicular. O True O False

A: Properties of rhombus: A quadrilateral is rhombus iff All four sides are equal. Diagonals bisect…

Q: Prove that ABCD with vertices 4(-1,3), B(-4,-1), C(1,-1), and D(4,3) is a rhombus assuming it is…

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Q: 2. Show that the points A(2,2,2), B(2,0,1), C(4, 1, – 1) and D(4, 3,0) are coplanar and that they…

A: The solution are next step

Q: Verify that the points are the vertices of a parallelogram, and find its area. A(1, 1, 3), B(5, -2,…

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Q: (c) Consider the parallelepiped with sides: u=(5,-2,1), v=(3, 2, 4), and w=(-6,1,1). V

A: Angle between two vector V and W found using cosine function

Q: Prove that quadrilateral GHIJ with the vertices G(-2,2), H(3,4), 1(8,2), and J(3,0) is a rhombus. YT…

A: solution: the objective is to determine whether the given vertices forms a rhombus

Q: Show that the quadrilateral with the given vertices is a parallelogram. E(-5,-2), F(-3, 3), G(3, 5),…

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Q: prove Theorem 4P.1 Theorem 4P.1 There are exactly six lines in the four-point geometry.

A: The known fact is that in four point geometry, any two distinct points have exactly one line on both…

Q: Use the diagonals to determine whether the parallelogram with the given vertices is a rectangle,…

A: Given: P(-5, 2)Q(4, 5)R(6, -1)S(-3, -4)

Q: If the diagonals of a parallelogram are perpendicular, then the parallelogram is a rhombus.

A: Given- The diagonals of  a parallelogram are prependicular . To show- That the parallelogram is…

Q: 22. In parallelogram ABCD, E and F are the midpoints of AB and CD, respectively. Prove that AECF is…

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Q: Show that the planes given by 2x − 4y − 3z = 5 and −4x + 8y + 6z = 1 are parallel, and find the…

A: Solution:Given2x − 4y − 3z = 5 −4x + 8y + 6z = 1To prove :The planes are parellel and to find the…

Q: Verify that the points A(0, 3, 2), B(1, 5, 5), C(6, 9, 5), D(5, 7, 2) are the vertices of a…

A: Given points are A(0,3,2), B(1,5,5), C(6,9,5), D(5,7,2).

Q: Prove that a parallelogram is a rectangle if and only if its diagonals are equal in length. (This…

A: Let ABCD be a parallelogram. Given AC and BD are diagonals of parallelogram in equal length. In…

Q: 6. Prove that quadrilateral LEAP with the vertices L(-3,1), E(2,6), A(9,5) and P(4,0) is a…

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Q: 7. Find the measures of the hyperbolic angles of the Euclidean square with vertices (0, 1), (0, 2),…

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Q: Prove that the diagonals on the parallelogram in the figure intersect at their midpoints. (b, c)…

A: let A=(b, c) B=( a+b , c) D=(0,0) C=(a,0)

Q: Verify that the points A(2, −3, 1), B(6, 5, −1), C(7, 2, 2), D(3, −6, 4) are the vertices of a…

A: Given: The points A2,-3,1, B6,5,-1, C7,2,2, D3,-6,4.

Q: Is of quadrilateral QRST intersect at P(-3,3). QRST has vertices at Q(4,7) and R(-4,5). What must be…

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Q: Find the measures of the angles between the diagonals of the rectangle whose vertices are A = (1,…

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Q: Consider a rectangular box below A (2,3, 5) 1.2 Find the length of the diagonal of the box…

A: O= (0,0,0) A=(2,3,5)

Q: Prove that the shape ABCD is a rhombus. With A(1, 4), B(3, 0), C(1. -4) and D(-1,0).

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Q: Prove that the quadrilateral with vertices A(0,0), B(4,3), C(7,-1) and D(3,-4) is a square.

A: →In a quadrilateral, if all sides are equal then quadrilateral is a square. →Calculate the length of…

Q: If A, B, C, and D are collinear, then they lie in the same plane. A, B, C, and D lie in the same…

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Q: 25. Prove analytically that the four diagonals joining opposite vertices of a rectangular…

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Q: How can we recognize if the two planes were parallel or not

A: Consider the vector equation of the two given planes as, r→·n1→=d1r→·n2→=d2 Here, n1→ and n2→ are…

Q: a parallelogram having a perpendicular diagonals is a rhombus.

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Q: Use Green's Theorem to evaluate $4x²ydx+2ydy where C is the triangle with vertices (0,0), (1,2), and…

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Q: Show that the points E(2, 2, 2), F(2, 0, 1), G(4, 1, -1) and H(4, 3, 0) are coplanar and that they…

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Q: Prove that if ABCD is a parallelogram, then its diagonals bisect each other.

A: Let us consider a paralellogram ABCD which have diagonals AC And BD and intersect at point E

Q: Verify that the points are the vertices of a parallelogram, and find its area. A(1, 1, 3), B(2,…

A: Given points, A(1,1,3) B(2,7,1) C(4,10,-6) D(3,4,-4) Let a,b,c,d, are position vectors of point…

Q: Prove that three points (x1, yl), (x2, y2) and (x3, y3) are collinear ( on the same straight line)…

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Q: 1. Prove that the diagonals on the parallelogram in the figure intersect at their midpoints. (b, с)…

A: Solve

Q: Prove that if two pairs of opposite edges of a tetrahedron are perpendicular, then the third pair is…

A: Consider the tetrahedron  ABCD and let two pairs of opposite sides are perpendicular. Consider the…