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2 November, 07:26

Which of the following statements is always true? (the first I put B, but I was not sure if I was correct) A. A parallelogram is a rectangle. B. A square is a rhombus. C. A rhombus is a square. D. A rectangle is a square.

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  1. 2 November, 07:56
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    The definitions of the quadrilaterals:

    A parallelogram is a quadrilateral which has two pairs of parallel sides.

    A rectangle is a quadrilateral which has two pairs of parallel sides and four right angles.

    A rhombus is a quadrilateral which has two pairs of parallel sides and all of sides are equal in length.

    A square is a quadrilateral which has two pairs of parallel sides, all of its sides are equal in length and all of its angles are right.

    Now look at your options:

    A:

    A parallelogram is a rectangle only when its angles are right, so it's not always true.

    B:

    A square always has four sides equal in length, so it's always a rhombus. Always true.

    C:

    A rhombus is a square only when its angles are right, so it's not always true.

    D:

    A rectangle is a square only when its sides are equal in length, so it's not always true.

    The correct answer is B.
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