Question

prove that every rhombus is a parallelogram pls give step by step solution ​

Answer 1

Answer:

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 opposite angles.

Answer 2

Answer:

Reason for statement 1: Given.

Statement 2:

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Reason for statement 2: Opposite sides of a rectangle are congruent.

Statement 3:

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Reason for statement 3: Given.

Statement 4:

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Reason for statement 4: Like Divisions Theorem.

Statement 5:

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Reason for statement 5: All angles of a rectangle are right angles.

Statement 6:

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Reason for statement 6: All right angles are congruent.

Statement 7:

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Reason for statement 7: Given.

Statement 8:

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Reason for statement 8: A midpoint divides a segment into two congruent segments.

Statement 9:

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Reason for statement 9: SAS, or Side-Angle-Side (4, 6, 8)

Statement 10:

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Reason for statement 10: CPCTC (Corresponding Parts of Congruent Triangles are Congruent).

Statement 11:

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Reason for statement 11: Given.

Statement 12:

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Reason for statement 12: If a triangle is isosceles, then its two legs are congruent.

Statement 13:

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Reason for statement 13: Transitivity (10 and 12).

Statement 14:

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Reason for statement 14: If a quadrilateral has four congruent sides, then it’s a rhombus.