A cube has four diagonals. Show that no two of them are perpendicular.

Q: Prove ABCD is a parallelogram. Justify mathematically and explain.

A: Given vertices of quadrilateral are A(-1,3) B(3,2) C(2,-5) D(-2,-4) Prove ABCD is a parallelogram

Q: Every rectangle is a parallelogram. O True OFalse

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Q: of a parallelogram are parallel and congruent. Opposite The of a parallelogram bisect each other.…

A: Fill the blanks

Q: Give an example of three planes,exactly two of which are parallel.

A: Give an example of three planes,exactly two of which are parallel.

Q: Show that the diagonals of a parallelogram are perpendicular if and only if it is a rhombus, i.e.,…

A: please find the attached solution

Q: All parallelograms have two pairs of parallel sides. O True O False

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Q: Write a two column proof to prove the following: If a transversal intersects two parallel lines,…

A: Given, Statement: If the transversal intersects two parallel lines then the bisectors of two…

Q: The diagonals of (not shown) are perpendicular. If one diagonal has a length of 10 and the other…

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Q: Find the area of a quadrilateral with vertices A( - 1 . - 1), 5(9, 4), C(20, 6).and D(10, 1).

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Q: If the diagonals of a parallelogram and congruent, what can you conclude regarding the…

A: Geometry: Since the diagonals of a parallelogram bisect each other, BE and DE are congruent and AE…

Q: A parallelogram is a quadrilateral with diagonals that bisect each other. O True O False

A: A Quadrilateral with diognals bisect each other is give below

Q: The diagonals of DABCD (not shown) are perpendicular. If one diagonal has a length of 10 and the…

A: Find perimeter of the parallelogram.

Q: Verify that the points are the vertices of a parallelogram, and then find its area.(1, −2, 0), (4,…

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Q: Prove that the diagonals of a parallelogram bisect each other.

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Q: If two consecutive sides of a parallelogram are perpendicular, then the diagonals are ____…

A: Query- If two consecutive sides of a parallelogram are perpendicular, then the diagonals are ____…

Q: Prove that a quadrilateral with vertices J(2,-1), K(-1,-4), L(-4,-1), and M(-1,2) is a square.

A: We have to prove that the quadrilateral given is a Square

Q: Prove that the diagonals of a rectangle are equal.

A: Let assume PQRS is the rectangle with                              PR and…

Q: A parallelogram has point symmetry about the point where its two diagonals intersect.

A: Given query is to find that given statement is true or false.

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: Every parallelogram has diagonals that bisect each other. O True O False

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Q: Show that a quadrilateral is a parallelogram if one pair of its opposite sides are equal and…

A: Consider a quadrilateral whose one pair of its opposite sides are equal and parallel.

Q: A parallelogram with congruent diagonals is a rectangle. O True O False

A: To explain the given statement

Q: Prove that the sum of the squares of the lengths of the sides of a parallelogram is equal to the sum…

A: Let the sides of the parallelogram be 'l' with longest and 'b' with shortest parallel lines and…

Q: Find measures of the angles between the diagonals of the rectangle whose vertices are A = (1,0), B =…

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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: a quadrilateral is a parallelogram if both pairs of its opposite sides are equal.

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Q: Prove that if a line bisects one side of a triangle and is parallel to a second side, then it…

A: Basic proportionality Theorem of triangle is define as if a line drawn parallel to one side of…

Q: Find the angle between the diagonal of a cube and an adjoining edge of the cube.

A: Given: Angle between the diagonal of a cube and an adjoining edge of the cube.

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

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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: Verify that the points are the vertices of a parallelogram, and find its area A( 1, 1, 3), B(-5, 7,…

A: let the points be A1,1,3 , B-5,7,1 , C-3,10,-6 , D3,4,-4 verify that the points are the vertices of…

Q: Theorem. The diagonals of a rectangle bisect each other and have the same length.

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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: For which quadrilaterals do the diagonals bisect each other, have the same length, and intersect at…

A: The geometrical figure that has four sides is called the quadrilateral. The rectangle, square,…

Q: When parallelograms are rectangles Prove that a parallelogram is a rectangle if and only if its…

A: Concept:   The calculus helps in understanding the changes between values that are related by a…

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

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Q: If both a parallelogram and triangle have the same base and altitude, then the area of the…

A: Given: If both a parallelogram and triangle have the same base and altitude, then the area of the…

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: 10 11 16 15 14 13 12

A: square forming

Q: If a quadrilateral is a parallelogram, then its diagonals a) bisect opposite angles. b) bisect each…

A: If a quadrilateral is a parallelogram, then its diagonals

Q: Show that quadrilateral RSTV with vertices R(- 5, - 3), S(1, – 11), T(7, -6), and V(1, 2) is a…

A: Solution: Consider the given that RSTV has vertices R(-5, -3) , S(1, -11), T(7, -6), and V(1, 2)…

Q: Which are parallel.

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

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Q: If a student claims that all figures with four congruent sides are squares. would he be correct?

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Q: If the diagonals of a rectangle are perpendicular, then the rectangle is a square.

A: Consider the given information as, If the diagonal of a rectangle are perpendicular, then the…

Q: Show that squares are the only rect-angles with perpendicular diagonals.

A: Consider u and v as the sides of the rectangle.The diagonals are perpendicular.Consider the…

Q: Verify that the points are the vertices of a parallelogram, and find its area. A(1, 1, 3), B(-5, 7,…

A:

Q: Prove that the diagonals of a rhombus (parallelogram with 4 equal sides) are perpendicular to each…

A: A parallelogram is a rhombus if all sides are equal.

Q: One pair of parallel sides proves a quadrilateral to be a parallelogram

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