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How to prove a quadrilateral a rhombus

Posted by Ayaz Parvez 4 years, 1 month ago

CBSE > Class 09 > Mathematics

1 answers

Utkarsh Kumar Shaw 4 years, 1 month ago

When proving a quadrilateral is a rhombus, we must know several things: 1) A rhombus is a parallelogram with equal side lengths. 2) A rhombus has diagonals that are perpendicular to one another and bisect one another. 3) A rhombus' diagonals bisect the angles of the vertices each diagonal intersects. Prove that when in a rectangle, the midpoints of the sides of the rectangle are drawn and labeled A,B,C, and D, then the quadrilateral ABCD is a rhombus. Say that the rectangle had side lengths of length e and f. Then the side lengths of quadrilateral ABCD, by the Pythagorean Theorem, are √(e2)2+(f2)2. Since all sides of this quadrilateral are equal then quadrilateral ABCD must be a rhombus.

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