Prove that the sum of the squares of the lengths of the sides of a parallelogram is equal to the sum of the squares of the lengths of the diagonals.

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: Can you show that this quadrilateral is a parallelogram?

A: We have to check

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: Prove analytically that the lengths of the diagonals of a rectangle are equal.

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Q: 5A. In quadrilateral ABCD, ∠B=∠D, ∠B= (2x+5)°, ∠A=3x and x=35°, prove that ABCD is a parallelogram.

A: We need to prove that ABCD is parallelogram.

Q: Find the angle between the diagonal of a cube and one of its edges.

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

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Q: 5. Find the length of the shorter diagonal in a rhombus with an area of 30 m² if the lengths of the…

A: Given: Area =30m2 length of diagonal differ by 4

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: Which statements about parallelograms are always true or sometimes true?

A: Six properties about parallelogram we need to remember : Opposite sides of parallelogram are…

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

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

Q: Prove that the sum ofthe squares of the sides of a rhombus s equal to the sum of the squares of its…

A:

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: What is the sum of the coordinates at which the diagonals of ABCD intersect?

A: From the given figure, The equation of the diagonals can be written as :

Q: Can you show that this quadrilateral is a parallelogram? yes

A: Parallelogram Definition A parallelogram is a quadrilateral with two pairs of parallel sides. The…

Q: Prove that if two lines are each perpendicular to a third line in the plane, then the two lines are…

A: Let slope of two lines are m1 and m2 and slope of third line is m3 . Now, as both lines are…

Q: Find the value of x that makes the quadrilateral a parallelogram. 2x + 3 x + 7

A: I have given an answer in step 2.

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: Consider rectangle RSTURSTU, where the diagonals of the rectangle intersect at point WW.   If…

A: Given problem:- Consider rectangle RSTU where the diagonals of the rectangle intersect at point W.…

Q: Find the volume of a parallelepiped if four of its eight vertices are A(0, 0, 0), B(1, 2, 0), C(0,…

A: Draw the diagram roughly

Q: Prove by the indirect method: “The length of a diagonal of a square is not equal in length to the…

A: Introduction: There are some basic methods that are used to prove any mathematical statement. These…

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

A: Apollonius's theorem   for triangle ABC with M being the midpoint of BC, the following equation…

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: Prove analytically that if the diagonals of a parallelogram rectangle. are equal, then the…

A: Given:-  Diagonals of parallelogram are equal.To proof  Parallelogram is a Rectangle.

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: How to find the value of x that makes m and n parallel

A:

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

A:

Q: For what value of x is the quadrilateral a parallelogram 3x 11 x+5

A:

Q: 5. Find the dimension of the largest rectangular building that can be placed on a right-triangular…

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Q: What value for X would guarantee that the quadrilateral shown is a parallelogram? 2x Зх + 2 5x – 6…

A: The parallelogram is a quadrilateral whose opposite sides are equal. It is observed that the length…

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: Prove that a parallelogram is a rhombus, a parallelogram with four equal sides, if and only if its…

A: Given : ABCD is a parallelogram              AB≅BC              AC⊥BD Prove : ABCD is a rhombus

Q: Prove that the diagonals of a trapezoid divide themselves proportionally.

A:

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 length of a side of a rhombus whose diagonals 48 cm and 14 cm long. are

A: Given, The diagonals of the rhombus are 48 cm and 14cm long. In the rhombus CB= 48 cm and AD= 14 cm…

Q: 10 11 16 15 14 13 12

A: square forming

Q: For any cyclic quadrilateral, the product of the diagonals equals the sum of the products of the…

A: Here we have to determine the name of the theorem. The given theorem is: For any cyclic…

Q: help!! the assignment is on quadrilaterals, similar triangles, and circles! I really need this…

A:

Q: Prove: If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle.

A: Statement: If the diagonals of a parallelogram are congruent, then the parallelogram is a rectangle.

Q: Prove that if semicircles are constructed on each of the sides of a right triangle, then the area of…

A: Area of semi circle having diameter of a is, Aa=πa222Aa=πa28         ...(1)  Area of semi circle…

Q: Find the value of and y quadrilateral is a parallelogram. so that the 2у — 11 y+3 3x 4x-3

A: In a parallelogram,  Diagonals bisects each other. So,  3x = 4x -3 => x = 3

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: %# 2 Find the coordinates of D for parallelogram QUAD. Q(3,-4), U(-2,-1), and A(1, 2)

A: Rule - diagonals of a parallelogram bisect each other.

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: how do i prove that the diagonals of a parallelogram bisect each other ? Then have to name…

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: If a side of a square has length 5 cm, then a diagonal of the square haslength _______ cm.

A: Here given a side of a square has length 5 cm