quadrilateral abcd is a parallelogram with diagonals that intersect at point e?
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Answer Expert Verified. Given: Quadrilateral ABCD is a parallelogram with diagonals that intersect at point E. AD and BC are parallelogram, this means that they are equal in measure.
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The diagonals are perpendicular to and bisect each other. A square is a special type of parallelogram whose all angles and sides are equal. Also, a parallelogram becomes a square when the diagonals are equal and right bisectors of each other.
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In the given figure, ABCD is a cyclic quadrilateral, in which AC and BD are its diagonals. ... In the given figure, ABCD is a cyclic quadrilateral, in which AC and BD are its diagonals. If ∠DBC = 60° and ∠BAC = 30°, then find ∠BCD.
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The diagonals of a parallelogram are not of equal length. They bisect with each other at the point of intersection with equal sides across the point of intersection. This can be proved using the ASA criterion as well. When we divide the parallelogram through two diagonals, we see that four triangles are formed.
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If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram, so if AP = CP and BP = DP, then the string forms a parallelogram. ALGEBRA Find x and y so that the quadrilateral is a parallelogram.
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ABCD is a rhombus whose diagonals intersect at O. If AB = 10 cm, diagonal BD = 16 cm, then find the length of other diagonal AC. Side of Rhombus are equal.
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ABCD is a quadrilateral P, Q, R, S are the points of trisection of the sides AB, CB, CD and AD respectively. Prove that PQRS is a parallelogram. ABCD is a quadrilateral in which P, Q, R, S are the points of trisection of the sides AB, CB, CD and AD respectively. ... Hence, PQRS is a parallelogram.
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The diagonal of a parallelogram PQRS are along the line x+3y=4 and 6x-2y=7. Then which geometrical figure (square, rhombus, rectangle) PQRS should be? ... => diagonals are perpendicular to each other.
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Answer. In a parallelogram if two diagonals are equal, then the parallelogram is a rectangle.So, ABCD is a rectangle.It is known that each interior angle of a rectangle is 90 degree. Since ABC is an interior angle of rectangle ABCD, so measure of angle ABC is 90 degree.
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Since opposite sides are equal in length, the squares on both diagonals are the same. We have already proven that a quadrilateral whose diagonals bisect each other is a parallelogram. Because ABCD is a parallelogram, its opposite sides are equal. (matching angles of congruent triangles).
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Definition A convex quadrilateral ABCD is called a ˆ parallelogram if the opposite sides AB, CD and BC, AD are parallel. A is a parallelogram having two adjacent sides rhombus congruent. A is a rhombus having two adjacent sides square perpendicular.
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A parallelogram is a quadrilateral whose opposite sides are parallel. The opposite angles of a parallelogram are equal. The opposite sides of a parallelogram are equal. The diagonals of a parallelogram bisect each other.
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In the given figure, ABCD is a rectangle, whose diagonals intersect at O. Diagonal AC is produced to E and Angle DCE = 145°.
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Proof: Given ABCD, let the diagonals AC and BD intersect at E, we must prove that AE ∼ = CE and BE ∼ = DE. The converse is also true: If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram. Theorem: Opposite angles of a parallelogram are congruent to each other.
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ABCD is a quadrilateral whose diagnonal AC divides it into two parts, equal in are, then ABCD. Solution : Here, ABCD need not be any of rectangle, rhombus and parallelogram because if ABCD is a square, then its diagonal AC also divides it into two parts which are equal in area.
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ABCD is a quadrilateral in which the bisectors of ∠A and ∠C meet DC produced at Y and BA produced at X respectively. ABCD is a quadrilateral in which the bisectors of ∠A and ∠C meet DC produced at Y and BA produced at X respectively. Prove that .
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Problem 2: A rectangle is sometimes a square. The diagonals of a parallelogram are sometimes congruent. The diagonals of a rhombus are always perpendicular. The consecutive angles of a parallelogram are never complementary.